Since we have been doing probability for the past few weeks so this week I am going to review how to work probability problems. I've already did a blog on probability so this should be really easy to remember. Blogging is so much fun!

Here's a few things that you will want to know about

Robability:

• If two events are mutually exclusive, then they cannot happen at the same
  time.
• P(A or B) = P(A) + P(B) - P(A & B).
• If the events are mutually exclusive, then P(A or B) = P(A) + P(B).

Know that we've reviewed some notes we can work a few examples!

Example 1: A standard deck of cards consists of 52 cards, with 13 cards in each of four suits (clubs, spades, diamonds, and hearts). Clubs and spades are always balck, while diamonds and hearts are always red. The face cards are the jacks, queens, and kings. If the deck is shuffled correctly, what is the probability that the card is:

• A black card = 26/52 = 1/2
• A red club = 0/52 = 0
• A card = 52/52 = 1
• An ace = 4/56 = 1/14

That's about it on probability. Hopefully you remembered everything!

Adiosssss!

Frommm carlayyyyyyyyy

Linear Inequalities

Linear inequalities is a rather simple concept to master and one should face no trouble with figuring out what the problem entails.

NOTE: If one divides or multiplies by negative (-) number, the sign must be reversed. THIS IS CRUCIAL TO OBTAINING THE RIGHT ANSWER!
> this stands for greater than
< this stands for less than
≤ this stands for less than or equal to
≥ this stands for greater than or equal to


Ex. 1:
5x+4<9
the x's goes on one side, while the integers go onto the other side
5x <5
you have to divide by 5
X <1 -This is the answer

-Sameer

Probability Review

This weekend I am going to review with you all the concept of probability. We were off of school all this week so it is time for a review lesson. Remember, there are a few things that you need to know about probability.

Notes:
• When events are mutually exclusive, then they cannot happen at the same time.
• When finding the probably of event A or event B follow the formula:
P (A or B) = P (A) + P (B) – P (A & B).
• When you find the probability of event A or event B and the events are mutually exclusive, then follow the formula: P (A or B) = P (A) + P (B).

Example: A standard deck of cards consists of 52 cards, with 13 cards in each of four suits (clubs, spades, diamonds, and hearts). Clubs and spades are always black, while diamonds and hearts are always red. The face cards are the jacks, queens, and kings. If the deck is shuffled correctly, what is the probability that the card is:

a. A diamond = 1/2
b. A red face card = 2/13
c. A jack = 1/13
d. A black heart = 0
e. A red or black card = 1

-Braxton

Something about probability

Soo since its been a long break and as usual i dont have my binder so im going to wing this one.

Im going to talk a little bit about probability.
Probability is the possible outcomes you can get when picking one thing from a group of things. Or you can even pull more than one thing. You can have the same thing more than once.
One way to express it would be P(event)

Say you have a die (which is one dice) you have the number 1 to 6
The probability of rolling a 3 would be 1/6
The probability of rolling an even number would be 3/6 which you would have to reduce to 1/2

Bam! thats it! Haha byeee

Probability

Things you should know:

• Two events can't happen at the same time when they are mutually exclusive.
• Formulas you need to know: P(A or B) = P(A) + P(B) - P(A & B). P(A or B) = P(A) + P(B).

Example 1: If you are given a standard 52 deck of cards, what is the probability that you will end up with a red card?

• Since half the deck is red that means you have 26 red cards.
• Your answer would be: 26/52 = 1/2.

Example 2: If you are given a standard 52 deck of cards, what is the probability that you will end up with a queen?

• Things you must know: four queens in a deck.
• Since it is out of 52, you answer will be: 4/52.
• That reduces to 1/13.
• Final answer: 1/13.

Example 3: What is the probability to get a red spade?

• Spades aren't red. They are black.
• Answer: 0/52 = 0.

Amber :)

CIRCLES

As always I will be taking advantage of the “post about whatever you want on holidays” rule. This week I’m going to talk about, drum roll please, CIRCLES!!!!!!
The standard form of a circle is (x-h)^2 + (y-k)^2 =r^2. (h,k) is the center and r is the radius.
To find the radius you can use the distance formula with the center and point on the outside or you can half the diameter found by using two points on the outside through the center.

To find the equation of a circle you must put it in standard form by completing the square.

1. Divide by leading coff., then move all numbers to the right

2. Half the middle term then square it and add both sides

3. Factor

When you graph in your calculator you need to slove for y and put a positive and negative formula in for y equals.

When you find the intersection of a line and circle
- solve the line for y
- plug circle equation for y
- slove th equadractic
- if you get i they DO NOT INTERSECT
(Please excuse my horrible note taking, I tend to be an idiot at the beginning of the school year and these notes are from August.)

EXAAAAAMPLEEEEEE TIIIIIIIIIIME
x^2 - 4x + y^2 + 6y + 4 = 0

subtract 4 from both sides (step one)
x^2 - 4x + y^2 + 6y = -4

half the middle term then square and add to both sides.
-4/2=(-2) ^2=4
6/2=3 ^2=9

x^2 - 4x + 4 + y^2 + 6y + 9 = -4 + 4 + 9

Factor
(x-2)^2 + (y+3)^2 = 9

Your center is (2,-3) and your radius is 3
THAT IS HOW YOU DO IT
See you guys tomorrow :/
--Sarah(:

16-2 probability of occuring events together

here is the second blog for this week. this blog is going to be a review on section 16-2 with probability of occuring events together. the formula that needs to be remembered is P(A and B) means you multiply the events together.so usually problems will be giving you the prbability of two events. the example will elaborate more on this

EX: fom a box containing 3 red balls and 5 green balls, 2 balls are randomley picked one after the other without replacement. find the pribability of each:

a) both balls are same color
P(RR) + P(GG)
3/8 * 2/7  +  5/8 * 4/7= 26/56 = 13/28

b) one is red one is green
P(RG) + P(GR)
3/8 * 5/7  +  5/8 * 3/7 = 30/56 = 15/28

16-1 probability

today i will be doing two blogs because thats how many i need to do to be caught up this week. this first blog is a review on 16 -1 probability. just to review mutually exclusive is P(A or B) = P(A) + P(B).  most of your answers will be in  fraction form so this is not really difficult. an aexample will be prvoided and show you the steps below.

EX: a card is drawn from a shuffled deck of 52
a) black card
26/52 = 1/2

b) a spade
13/52 = 1/4

c) not a spade
52-13 = 39
39/52 = 3/4

Review of Probability

Okay, so this week I am going to review how to work probability problems. Since I already went over this a few weeks ago, it should be very easy. So first, you need to know a few things.

Notes:

• If two events are mutually exclusive, then they cannot happen at the same
  time.
• P(A or B) = P(A) + P(B) - P(A & B).
• If the events are mutually exclusive, then P(A or B) = P(A) + P(B).

Okay, so now that you know the few notes, I am going to work a few examples for you to better understand.

Example 1: A standard deck of cards consists of 52 cards, with 13 cards in each of four suits (clubs, spades, diamonds, and hearts). Clubs and spades are always balck, while diamonds and hearts are always red. The face cards are the jacks, queens, and kings. If the deck is shuffled correctly, what is the probability that the card is:

• A black card = 26/52 = 1/2
• A red club = 0/52 = 0
• A card = 52/52 = 1
• An ace = 4/56 = 1/14

Well that's how you work probability problems. Have a great weekend. Byeeee

--Halie!

17-3

Review of Variance and Standard Deviation
In this lesson, we learned about the statistics variance and standard deviation, which are both used to describe the spread of data about the mean.
- s & o = standard deviation
- s^2 = variance
- E = sum
- xi = numbers
- n = how many you have
- x(with a line over it) = mean
- standard deviation formula: s = sq. root of (E(xi^2)/n) -x^2

Example 1: Find the standard deviation of the data 1, 7, 9, 15.

• n=4; x=8; E(xi^2)=356 *I just listed how many numbers there are(4), the mean(8), and the sum(356). Now I use these numbers to plug into the formula.


• sq. root of (356/4)-4


• answer: s^2= 25; s= 5 *I just divided 356 by 4 and subtracted 64 to get 25 to get the variance(25), and then took the square root to find the standard deviation(5).

linear inequalities

This week we learned about linear inequalities. The concept is extremely simple so you all should catch on rather quickly. Let’s start with the simply facts that you need to know for this particular lesson.

If you divide or multiply by a negative number, you must reverse the sign. It is VERY important that you do not forget to change the sign.

> this sign means greater than
< this sign means less than
≤ this sign means less than or equal to
≥ this sign means greater than or equal to

You will solve the equation just like any other. I usually just pretend that the inequality is an equal sign. This idea will help when working through the steps in your head.

EXAMPLE:
2x-8 > -2x
Move the x’s to one side, the integers to the other.
4x > 8
Next, you divide by four.
X > 2

That’s how it’s done.
--Sarah(:

Linear Equations

Things you should know:

• When you divide or multiply by a negative number, you must reverse the sign.
• > means greater than
• < means less than
• ≤ means less than or equal to
• ≥ means greater than or equal to

Example 1 9x+16<48

• To solve this problem, you must get x by itself.
• First you will have to subtract 16.
• That leaves you with 9x<32.
• Now you have to divide by 9.
• That leaves you with x<32/9.
• You answer is x<32/9.

Example 2 -4x+12>50

• Again you have to solve for x.
• First you have to subtract 12
• That leaves you with -4x>38
• Divide by -4
• That leaves you with x<-19/12.
• Since it was a negative number that you were dividing by, you have to change the sign.
• Final answer: x<-19/12

Amber :)

3-1 Linear Inequalities

Okayy, so this week I am going to explain how to solve linear inequalities problem. This is really easy. All it is, is basic algebra. There is only one or two different things. So first let me tell you some things you need to know.

Notes:

• If you divide or multiply by a negative number, you must reverse the sign
• > this sign means greater than
• < this sign means less than
• ≤ this sign means less than or equal to
• ≥ this sign means greater than or equal to

Okay, so now that you know everything you need to, I am going to work a few examples for you to better understand the process.

Example 1: -2x > 4

• You need to get x by itself.
• To do this you must divide by x.
• Since 2 is negative you are going to change the inequality sign.
• So you answer is going to be x < -2.

Example 2: 5x + 3 > 28

• You need to get x by itself.
• The first thing you need to do is subtract 3 from both sides.
• That would give you 5x > 25.
• Then you would divide both sides by 5.
• Since 5 is positive, you keep the inequality sign just as it is.
• Your answer is going to be x > 5.

And that is how you work these kind of problems. It is super easy! Well that's it for this week. Happy Mardi Gras!! :D

--Halie

So I have like 5 minutes to do this blog and i'm sitting in ihop. I've been here for like two hours and still haven't gotten my food. It sucks. Anyways, imma teach y'all how to solve inequalities. So it's pretty simple. You do the same thing as a normal equation. The only difference is if you divide by a negative you switch the inequality sign.

So now for an example.

Example 1: 5x<10

You would get x<2

Example 2. -2x>4

After switching the signs you would get x<-2.

Inequalities are pretty simple. They're no harder than a simple equation.

That's about it on I equalities. I really hope this was 160 words

Happy mardi grad

Carlayyy

3-1 Linear Inequalites, Absolute Value

This weekend I am going to teach you all how to solve linear inequalities. Some of these inequalities contain absolute values. This lesson only contains linear inequalities with one variable. To solve these equations, you just have to use basic algebra. There are a few things that you need to know about inequalities.
Notes:
· If you divide or multiply by a negative number, you must reverse the sign
· > this sign means greater than
· < this sign means less than
· ≤ this sign means less than or equal to
· ≥ this sign means greater than or equal to
Example 1: 5x + 3 > 28
· You would subtract 3 from both sides, which would give you 5x > 25
· Then you would divide both sides by five
· Your final answer would be: x > 5
Example 2: 4 – 6x < 16
· You would subtract 4 from both sides, which would give you -6x < 12
· Then you would divide both sides by -6 and flip the sign
· Your final answer would be: x > -2


-Braxton

3-1

3-1 Linear Inequalities; Absolute Value

In this lesson, we learned how to solve and graph linear inequalities with one variable. Solving linear inequalities is very similar to solving linear equations.

-You can add/subtract the same number to both sides of an inequality.

-You can multiply/divide both sides of an inequality by the same positive number.

-You can multiply/divide both sides of an inequality by the same negative number if you reverse the inequality sign.

Example 1: 8x + 6 > 30

• 8x > 24 (I subtracted the 6 from 30.)
• x > 3 (I divided 24 by 8.)

Example 2: lxl > -2

• x > -2 x < 2

Example 3: 3x - 4 < 10 + x

• 3x < 14 + x (I added the 4 to 10.)
• 2x < 14 (I subtracted the x from 3x.)
• x < 7 (I divided 14 by the 2.)

Chapter 10 Throwback!

Chapter 10 was all about formulas. These are the formulas from chapter 10 section 1. Note: the trig chart will be needed as well throughout the entire chapter. The formulas are very specific and must be followed accordingly. If one memorizes these formulas, the chapter becomes fairly easy.
Formulas

cos(alpha +/-beta)=cos alpha cos beta-/+sin alpha sin beta

sin x+sin y=2sinx+y/2 cos x-y/2

sin (alpha+/-beta)=sin alpha cos beta+/-cos alpha sin beta

sin x-sin y=2cosx+y/c sin x-y/2

cos x-cos y=-2sinx+y/2 sin x-y/2

cos x+cos y=2cosx+y/2cosx-y/2

All you have to do is REPLACE the angle measures with the numbers from the trig chart.

Ex: 1 Find the exact value of Sin 75
1. sin 75 is not on the trig chart, so a formula must be picked for use
2. So one will use Sin(45+30)
3. When expanded, it looks like Sin45 cos 30+cos 45 sin30
4. Using the trig chart, you get Sqrt 2/2 x sqrt 3/2 + Sqrt 2/2 x sin 1/2
5. Now all that is left is simplifying the answer.It comes out to be

(sqrt 6+sqrt 2)/4

-Sameer

Ahh blogging

This week we spent some time covering standard defiance. It seems like it's overwhelming but it really is not. All you need to know is what each letter stands for and boom you are pretty much good to go baby! Anyway here it is.



The formula used for these problems is s^2 = ((∑(xi^2)) / (n)) - x̅ ^2

When you see the symbol ∑ it means the sum.

The symbol xi stands for the numbers.

x̅ stands for the mean of the numbers.

The letter n stands for the amout of numbers being used in the problem.

The easiest way to work with standard deviance is to set up two columns for xi and xi^2. You have to find each part before plugging into the formula and working the problem. Also the variance is written as s^2.

EXAMPLE TIME

Find the standard deviance of 1,2,3,4,5

First set up your chart

Xi-xi^2
1-1
2-4
3-9
4-16
5-25

n=5

Now plug into the formula.

S=square root of

--Sarah (:

16-4

today im showing you how to do probability with combinations. its kind of hard to explain this method without showing an example. you have to use the combinaion formula which is (n! / (n-r)! r!). usually this type of stuff will be dealing with more than one thing such as a 52 deck of cards and dice and things of that sort. it will be really easy to explain once i show the examole below. so here we go.


EX: free concert tickets are distributed to 4 students chosen at random from 8 Jrs. and 12 Srs. in the school orchestra. what is the probability that free tickets are recieved by:
a) 4 senoirs
first put in combination form: 12 C 4 / 20 C 4
it is like this because there are 12 senoirs and your choosing 4 andd there is a total of 20 people
this is your answer in combination form.

b) exactly 3 seniors
put in combination form: 12 C 3 * 8 C 1 / 20 C 4
this is your answer in  combination form because your choosing 3 senoirs and multiply by it the chance of getting one junior over the total

c) exactly 2 senoirs
12 C 2 * 8 C 2 / 20 C 4
combination form answer ^

d) exactly 1 senior
12 C 1 * 8 C 3 / 20 C 4
combination form answer ^

e) no seniors
8 C 4 / 20 C 4
combination form answer ^

standard deviation and variance

soo this week we learned about standard deviation and variance. I am going to show you a few important things you need to know in order to do these types of problems. So here are the formulas.

• The formula used for these problems is s^2 = ((∑(xi^2)) / (n)) - x̅ ^2
• When you see the symbol, ∑ it means the sum.
• The symbol xi stands for the numbers.
• x̅ stands for the mean of the numbers.
• The letter n stands for the amout of numbers being used in the problem.
• When working these problems, you might find it easier by setting up a chart with two columns.
• Also, when working these problems, you might find it easier by finding everything first then plugging it into the formula given above.

So now that i have showed you the information you need to know i will show you how to do a problem.

Example 1: Find the standard deviation of 5, 5, 7, 8, and 10.

• The first thing you are going to do is find everything.
• n is going to be 5.
• x̅ is going to be 7.
• ∑(xi^2) is going to be 263
• Once you find everything you can, you plug it into the formula.
• Your answer is going to end up being 1.897

and thats how you work it!!

We have been working on probability stuff over the two weeks. It had been a blast! Probability is pretty much statatics. It tells you what the odds or chances of something happening or not happening will be. Your answer will always be in between 0-1 and is also a fraction. The final answer of your fraction should be simplified. Some of the most common types of probability is dealing with dice or a deck of cards. I'm going to show you an example of each.

Example 1. What are the odds of drawing a diamond or a club out of a standard deck of 52 cards.

They're 13 diamonds and 13 clubs in a deck of cards. So you would put 13/52 + 13/52 which simplifies to 1/2. That would be your final answer.

Example 2. What are the odds that you roll higher than a a multiple of 2 when rolling a six sided die

Since there are 3 sides that are multiples of 2(2,4,6) and six total sides you would do 3/6 which simplifies to 1/2. That would be your final answer.

Probability is pretty easy once you get used to it.

Make it a great day or not, the choice is yours :)

Carley

Standard Deviation and Variance

Okay, so this week I am going to teach you how to work problems using standard deviation and variance. This might seem hard at first but it really easy after you know what everything stands for you. So first your going to need to know a few things.

• The formula used for these problems is s^2 = ((∑(xi^2)) / (n)) - x̅ ^2
• When you see the symbol, ∑ it means the sum.
• The symbol xi stands for the numbers.
• x̅ stands for the mean of the numbers.
• The letter n stands for the amout of numbers being used in the problem.
• When working these problems, you might find it easier by setting up a chart with two columns.
• Also, when working these problems, you might find it easier by finding everything first then plugging it into the formula given above.

Okay, so now that you know the basics of working these problems, I am going to work an example for you.

Example 1: Find the standard deviation of 5, 5, 7, 8, and 10.

• The first thing you are going to do is find everything.
• n is going to be 5.
• x̅ is going to be 7.
• ∑(xi^2) is going to be 263
• Once you find everything you can, you plug it into the formula.
• Your answer is going to end up being 1.897

And that's it for this week. BYEE.

--Halie

17-3 Standard Deviation and Variance

This weekend I am going to teach you all how problems that ask you for standard deviation and variance. Before I show you all an example of a problem like this, there are a few things that you need to know.
Notes:
• When you see the symbol, ∑ (sigma), it means the sum
• When you see xi, it is the numbers
• When you see n, it is how many numbers you have
• When you see x̅, it is the mean of the numbers
• The formula is: s^2 = ((∑(xi^2)) / (n)) - x̅ ^2
• When you are solving for standard deviation, you look for three things: n, x̅, and ∑(xi^2)
• You do this by setting up a chart with two columns; s and s^2
• The numbers are given to you in the problem
• After you find those three things, you just plug in and simplify
Example: Find the standard deviation of 5, 5, 7, 8, and 10
n= 5
x̅= 7
∑(xi^2)= 263

S= sq. root of ((263/5) – 49)
S= sq. root of (3.6)
S= 1.897

-Braxton

16-4

16-4 Probability Problems Solved With Combinations

In this lesson, we use two different methods to solve probability problems. Method 1 uses conditional probability. Method 2 uses combinations, and it can be used to solve problems that are not readily solved using method 1.

Example 1: Five cards are drawn at random from a standard deck. Find the probability that all 5 cards are hearts using conditional probability.

-13/52 x 12/51 x 11/50 x 10/49 x 9/48 = 33/66,640

Example 2: Three marbles are picked at random from a bag containing 4 red marbles and 5 white marbles. What is the probability of all three marbles being red? Find using the combination method.

- 4C3 x 5C0/9C3

Example 3: Free concert tickets are distributed to 4 students chosen at random from 8 juniors and 12 seniors in the school orchestra. What is the probability that free tickets are received by exactly 2 seniors?

-12C2 x 8C2/20C2

Over the week we started chapter 16. It was all about different types of probability. The two most popular types (that we used anyway) had to do with a standard deck of cards or with rolling two dice.

When working with probability, your answer will almost always be a fraction. There are two exceptions to this. If the event is absolutely impossible, the answer is zero. If the event is going to happen no matter what, the answer is one. Your answer can also be expressed as a percent.

The formula for probability is as follows:
P(event eight)= number of favorable outcomes/total number of outcomes

Here is another formula:
P(A or B)=P(A)+P(B)-P(A and B)

If something is mutually exclusive, it is impossible for both events to happen at the same time. The formula for something that is mutually exclusive is as follows:
P(A or B)=P(A)+P(B)

EXAMPLE:
A standard deck of cards has suits: spades, hearts, clubs, and diamonds. Each suit has thirteen cards. Of those cards, nine have numbers, three have faces, and one is an ace. What is the probability that you pick a card that is
A) An even number
P(even number)=5/52

B) A black card
P(black card)=26/52 = ½

C) A red spade
P(red spade) 0/52=0

--Sarah

16-1

I will teach on how to find the probability of one event or either of two events.

P(event A) = # of favorable outcomes/total # of possible outcomes

P(A or B) = P(A) + P(B) - P(A & B)

P(A or B) = P(A) + P(B)( if it is mutually exclusive)

Ex 1: A standard deck of cards with 13 cards each of four suits which are diamonds, spades, clubs, and hearts. Clubs and spades are black, and diamonds and hearts are red. Assuming the deck is shuffled properly what would be the probability that the top card is:

a) a red card

=26/52 = 1/2

b) a black face card

=6/52 = 3/26

c) a 4, 5, or 6 card (any suit)

=12/52= 3/13

Example 2: An integer between 9 and 15, inclusive, is picked randomly. What would be the probability that the integer is:

a) divisible by -3

= 0/7=0

b) odd

= 4/7

c) even

= 3/7

-Sameer

Probablity

We learned probability over the past week or so and it's a really simple concept which I'm sure some - if not all - of us already knew. With probably, you basically take the fraction of the total and divide it by the total number and simply if you must.

Example: There are 2 green marbles, 4 red marbles, and 274 clear marbles ;)... what is the probability of picking up a red marble? *Picks up calculator*
4/ 280 = 1.4 x 10^ -2


Well... that's it for probability... going read "The Road" now..

~ Parrish Masters

Probability

So, over the past week we learned different types of probability. Probability is part of statatics. It tells you the odds or chances of something happening or not happening. It's always in between 0-1 an is in a fraction. The final answer of your fraction should be simplified. Some of the most common types of probability is dealing with dice or a deck of cards. I'm going to show you an example of each.

Example 1. What are the odds of drawing a diamond out of a standard deck of 52 cards.

They're 13 diamonds in a deck of cards. So you would put 13/52 which simplifies to 1/4. Thatvid your final answer.

Example 2. What are the odds that you roll higher than a four when rolling a six sided die

Since there is two sides higher than 4 and six total sides you would do 2/6 which simplifies to 1/4.

That's about all probability is. It's pretty easy.

That's it, carleyyyy

Probability

Ok so today im going to teach you a little about probability. The probability is the possible outcomes that something can happen. One way to express the probability is p(event). I think that this section is really easy and will just go straight and show you a few examples because it isnt that hard to understand.

So this will be out of a standard deck of cards. The first thing you will need to understand a deck of cards.

52 cards.
26 red cards
26 black cards.
4 suits
clubs spades hearts dimonds
13 in each suit
the suit consist of an ace 1 2 3 4 5 6 7 8 9 10 jack queen king
jack queen and king are face cards.

* Now that i have explain to you the standard deck of cards i will work a few problem.

p(black cards) = 26/52 This will reduce to 1/2 it is very important to make sure you reduce the fractions.

p(a 2or3)= 2/13

P(facecard)= 12/52 3/13

*another example can the the probability of rolling a die*
consist of numbers 1-6

P(even) 1/2

P(odd) 1/2

P(123or4) 2/3

BAM!!!!!!!

Probability

Things you need to know:

• Probability is from 0-1, which means 0 is the probability it will not happen and 1 is the probability it will happen.
• Formula: P(event A) = favorable outcomes/total outcomes
• Most probability problems involve a standard deck of cards or the rolling of one or two dice. Those are the most common types.

Example 1: Out of a standard deck of 52 cards, what is the probability that you will get a red card.

• First you need to know how many red cards are in a deck of 52 cards.
  
• There are 26 red cards in a deck of 52 cards.
• So you would just put that as a fraction: 26/52.
• After that you can reduce it. It reduces to 1/2.
• Final answer: 1/2.

Example 2: Out of a standard deck of 52 cards what is the probability that you will get a black diamond.

• First you must realize that there is not a black diamond in a 52 deck of cards.
• It does not exist.
• So since it does not exist you would put 0/52.
• 0/52 will give you 0.
• 0 is your final answer.

-Amber :)

16-1

This weekend I am going to teach you all how to find probabilities. This lesson is just simple probabilities, like finding the probability of either one or two events. There are a few things that you need to know before I show you all an example.

Notes:
• If two events are mutually exclusive, then they cannot happen at the same time.
• P(A or B) = P(A) + P(B) - P(A & B)
• If the events are mutually exclusive, then P(A or B) = P(A) + P(B)

Now I will show you all an example of a probability problem.

Example: A standard deck of cards consists of 52 cards, with 13 cards in each of four suits (clubs, spades, diamonds, and hearts). Clubs and spades are always black, while diamonds and hearts are always red. The face cards are the jacks, queens, and kings. If the deck is shuffled correctly, what is the probability that the top card is:

a. a black diamond: 0/52 = 0

b. a face card: 12/56 = 3/14

c. an ace: 4/56 = 1/14


-Braxton

16-1

16-1 Finding Probabilities

In this lesson, we learn how to find the probability 0f an event or either of two events.

-P(event A) = favorable outcomes/total # of outcomes

-P(A or B) = P(A) + P(B) - P(A & B)

-P(A or B) = P(A) + P(B) *mutually exclusive*

Example 1: A standard deck of cards consists of 52 cards, with 13 cards in each of four suits (clubs, spades, diamonds, and hearts). Clubs and spades are always black, while diamonds and hearts are always red. The face cards are the jacks, queens, and kings. If the deck is shuffled correctly, what is the probability that the top card is:

a) a red ace

=2/52 = 1/26

b) not a red ace

=50/52 = 25/26

c) a spade face card

=3/52

Example 2: One of the integers between 11 and 20, inclusive, is picked at random. What is the probability that the integer is:

a) even

= 1/2

b) divisible by 3

= 3/10

c) a prime

= 4/10 = 2/5

16-1 Probability

So this week I am going to explain how to work probability problems. They are superrr easy, but first I need to tell you a few basic things that you might need to knoww.

• Probability is from 0-1, which means 0 is the probability it will not happen and 1 is the probability it will definetaly happen.
• There is only one formula you need to know when working these types of problems. That formula is : P(event A)= favorable outcomes / total outcomes
• Most probability problems involve a standard deck of cards or the rolling of one or two dice. Those are the most common types of problems you will see.

So now that you know all that, I will work a few examples for you.

Example 1: Out of a standard deck of 52 cards, what is the probability that you will get a black card.

• In a deck of 52 cards there are 26 total black cards.
• So you would put 26/52.
• Which that then reduces into 1/2 and that is your answer.

Example 2: Out of a standard deck of 52 cards, what is the probability that you will get a black or red card.

• In a deck of 52 cards all they have are black and red cards.
• So you would put 52/52.
• Which reduces into 1. So you then know that your chances of getting a black or red card will definetaly happen.

And that is how you work probability problems. So that's it for this weeek. BYEEE :)

--Halie.

16-1 probability

today im teaching you how to find the probability of things. these things mostly include a 52 deck of cards or rolling dice. there are other things you can get probability of but these are the main two we will be dealing with. probabilty is from 0-1 meaning 0 will not happen 1 meaning will happen. the fromula for this is             P(event A)= favorable outcomes / total outcomes. this is really easy and has been done before so here is an example below.



EX: find the probability of each picking out of a 52 card deck that is shuffled well.

a) a black card
26 black cards / 52 total cards = 1/2 is the probabilty

b) a spade
13 spades / 52 cards = 1/4 is the probability

c) not a spade
39 not spades / 52 cards = 3/4 is the probability