Question

1. A collection of 12 rare coins contains 4 counterfeits. If three coins are randomly selected from the collection and sent to a dealer, find the probabilities that: a) none of the coins sent to the dealer are counterfeit. b) at least 2 of the coins sent are counterfeit.

Answer 1

Let p be the probability that the selected coin is a counterfeit. Then p = 4/12 = 1/3 = 0.333333

a) P(none of the selected coin is a counterfeit)

= P(1st coin is not counterfeit) * P(2nd coin is not counterfeit) * P(3rd coin is not counterfeit)

= (1-1/3) * (1-1/3) * (1-1/3)

= 2/3 * 2/3 * 2/3

= 8/27

= 0.2963

b) P(at least 2 of the coins sent are counterfeit)

= 3 * P(two of the three coins is counterfeit) + P(all 3 coins are counterfeit)

= 3 * 1/3 * 1/3 * 2/3 + 1/3 + 1/3 + 1/3

= 2/9 + 1/27

= 7/27

= 0.2592

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