Consider a bag that contains 225 coins of which 4 are rare Indian pennies. For t

Question

Consider a bag that contains 225 coins of which 4 are rare Indian pennies. For the given pair of ovents A and B. complete parts (a) and (o) below. A: When one of the 225 coins is randomly selected, it is one of the 4 Indian pennies B: When another one of the 225 coins is randomly selected (with replacement), it is also one of the 4 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 O A. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other O B. The two events are dependent because the 5% guideline indicates that they may be treated as dependent. O C. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other D. The two events are independent because the 5% gudeline indicates that they may be treated as independent. b. The probability that events A and B both occur is (Round to six decimal places as needed.) Click to select your answerls)

Explanation / Answer

Solution;

a) option A

b) the probability that both the events A and B occur = P(A) *P(B)  = 0.000313

total number of coins = 225

number of rare indian pennies = 4

Proabability of picking an indian penny from the given 225 coins P(A) = 4 / 225 = 0.0177

Probability of picking another indian penny form the given 225 coins (with replacement)P(B) = 4 / 225 = 0.0177

the occurance of one doesn't affect the probability of the occurance of the other, hence the events are indepent.

the probability that both the events A and B occur =

= P(A) *P(B)

= 0.0177 * 0.0177

= 0.000313

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