Consider a bag that contains 216 coins of which 6 are rare Indian pennies. For t

Question

Consider a bag that contains 216 coins of which 6 are rare Indian pennies. For the given pair of events A and B. complete part, (a) and (b) below. A: When one of the 216 coins is randomly selected, it is one of the 6 Indian pennies. B: When another one of the 216 coins is randomly selected (with replacement), it is also one of the 6 Indian pennies. a. Determine whether events A and B are independent or dependent. b. Find P (A and B). the probability that events A and B both occur. a. Choose the correct answer below. A. The two events are dependent because the 5% guideline indicates that they may be treated as dependent. B. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other. C. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other. D. The two events are dependent because the 5% guideline indicates that they may be treated as independent.

Explanation / Answer

Event A : One of the 216 coins is randomly selected, it is one of the 6 Indian pennies B : When another one of the 216 coins is randomly selected (with replacement), it is also one of the 6 Indian pennies a)   Events A and B follow Binomial probability Distribution Sample size = 6 rare Indian pennies The sample size is 2.78 % which is less than 5% Hence the 5% guideline for Binomial Probability Distribution holds here Answer : D. The two events are independent because the 5% guideline indicates that they may be treated as independent. b) Ways in which one coin is selected from the bag = 216C1 Ways in which one rare Indian penny is selected from the bag = 6C1 P(A) = P(One of the 216 coins is randomly selected, it is one of the 6 Indian pennies)         = 6C1 / 216C1         = 6 / 216         = 0.0278 P(B) = P(When another one of the 216 coins is randomly selected (with replacement), it is also one of the 6 Indian pennies) Since the selection is with replacement, P(B) =         = 6C1 / 216C1         = 6 / 216         = 0.0278 Since A and B are independent events P(A and B) = P(A) * P(B) =     0.0278 * 0.0278 = 0.000773 P(A and B) = 0.000773

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