Answer:
(a) Event A and B are independent.
(b) Probability = 0.0816
The correct answer from the choices:
D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other
Step-by-step explanation:
Total coins = 231
Indian pennies in the the total coins = 66
Probability of Event A : Number of Indian pennies / total number of coins
66 / 231 = 0.2857
Probability of Event B : Number of Indian pennies / total number of coins
66 / 231 = 0.2857
(a) Since the coins are picked WITH replacement, the events are independent. As picking a coin does not change the probability of the next coin being picked. This is proven by how Event B has the same probability as Event A.
Thus, the answer to this part is D. 'The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.'
(b) The probability that both events occur will be their respective probabilities multiplied together. This is:
Total Probability = Probability of A * Probability of B
Total Probability = 0.2857 * 0.2857
Total Probability = 0.0816