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Probability Chapter 11 1

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Counting Techniques and and Probability Section

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Examples Helen and Patty both belong to a club of 25 members. A committee of 4 is to be selected at random from the 25 members. Find the probability that both Helen and Patty will be selected. 3

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Examples A piggy bank contains 2 quarters, 3 nickels, and 2 dimes. A person takes 2 coins at random from this bank. Label the coins Q 1, Q 2, N 1, N 2, N 3, D 1, and D2D2 so they can all be regarded as different. Then find the probabilities that the values of the 2 coins selected are the following: a. 35¢b. 50¢ 4

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Examples Assume that 2 cards are drawn in succession and without replacement from an ordinary deck of 52 cards. Find the probability that a. 2 kings are drawn. b. 1 spade and 1 king other than the king of spades (in that order) are drawn. 5

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Examples If 2% of the auto tires manufactured by a company are defective and 2 tires are randomly selected from an entire weeks production, find the probability that neither is defective. 6 Find the probability of at least 1 of the 2 selected tires is defective.

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Example A box contains 10 computer disks and 2 are defective. If 3 disks are randomly selected From the box, find the probability that exactly 2 are defective. 7 defective good total

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Examples A hat contains 24 names, 13 of which are female. If seven names are randomly drawn from the hat, what is the probability that at least one male name is drawn? In a sample of 32 hand-held calculators, 26 are known to be nonfunctional. If 21 of these calculators are selected at random, what is the probability that exactly 17 in the selection are nonfunctional? Round to the nearest thousandth. 8

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Example When printing color inserts for newspapers, it sometimes happens that the registration of the print colors is imperfect. (This results in the different colors not being aligned properly, so the image is blurry.) Suppose that in a run of 1217 one-page inserts, 78 have registration errors. If 4 inserts are chosen at random, what is the probability that at least one of them has a color registration error? 9

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Example A bag contains 5 red marbles, 6 blue marbles, 11 white marbles and 9 yellow marbles. You are asked to draw 5 marbles from the bag without replacement. What is the probability of drawing less than two yellow marbles? 10 END

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