Question

Mark plays field hockey. He makes a goal 55% of the time he shoots. A = the event Mark is successful on his first goal attempt. P(A) = 0.55. B = the event Mark is successful on his second goal attempt. P(B) = 0.55. Mark tends to make goals in streaks. The probability that he makes a second goal given that he made the first goal is 0.80.

Which of the following is true about A and B?
A and B are independent and mutually exclusive

A and B are neither independent nor mutually exclusive

A and B are independent, but not mutually exclusive

A and B are not independent, but mutually exclusive

A and B are disjoint

Answer 1

Answer: A and B are not independent, but mutually exclusive.

Explanation:

Independence means that the probability of one event happening does not affect the probability of the other event happening. Mutual exclusivity means that the two events cannot happen at the same time.

In this case, we know that P(B|A) = 0.80, which means that the probability of Mark making a second goal given that he made the first goal is 0.80. This is different from P(B) = 0.55, the probability of Mark making a second goal without any information about whether he made the first goal. This means that the probability of event B is affected by whether event A has occurred, so A and B are not independent.

However, A and B are mutually exclusive, because Mark can either make his first goal or not, but can not make it at the same time.