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