Exercise 12 Page P19

We are finding the probability of choosing two action DVDs followed by a comedy DVD. Since we do not put the DVD back on the shelf before we pick the next one, the picks are not independent. We can use the Probability of Dependent Events rule to find the probability. The probability P(2action, then comedy) is the product of the following three probabilities: P(1st action) P(2nd action| 1st action) P(3rd comedy| 1st action and2nd action) There are 8+3+5= 16 DVDs on the shelf, and 8 of these are action DVDs. We select at random, so the DVDs are equally likely to be picked. Hence, the probability of picking an action DVD first is the ratio of the number of action DVDs to the total number of DVDs.

P(1st action)=8/16=1/2 This action DVD is not put back on the shelf, so before the next pick there are 16-1= 15 DVDs on the shelf, and 8-1= 7 of these are action DVDs. We need to use these new numbers to calculate the probability of the second pick. P(2nd action| 1st action)=7/15 This second DVD is not put back on the shelf either, so before the third pick there are 15-1= 14 DVDs left on the shelf. Since none of the first two picks are comedy DVDs, there are still the original 3 comedy DVDs on the shelf. We need to use these numbers to calculate the probability of the third pick. P(3rd comedy| 1st action and2nd action)=3/14 The answer to the question is the product of the three probabilities we found. P(2action, then comedy)=1/2*7/15*3/14=1/20 The probability of picking an action DVD twice in a row and then a comedy DVD without replacement is 120=0.05.

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