Carlos plays college soccer. He makes a goal 65% of the time he shoots. Carlos is going to attempt two goals in a row in the next game.
A = the event Carlos is successful on his first attempt. P(A) = 0:65. B = the event Carlos is successful on his second attempt. P(B) = 0:65. Carlos tends to shoot in streaks. The probability that he makes the second goal GIVEN that he made the first goal is 0.90.
Answer the following questions.
Are A and B independent? Please provide reasoning for your answer.
Are A and B mutually exclusive? Please provide reasoning for your answer.