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
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