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.

If Mark attempts two goals, what is the probability that he makes both goals?

Answer 1

We can use the formula for conditional probability to find the probability that Mark makes both goals:

P(A and B) = P(A) * P(B | A)

We know that:

P(A) = 0.55 (the probability that Mark makes a goal on his first attempt)

P(B | A) = 0.80 (the probability that Mark makes a goal on his second attempt given that he made the first goal)

So:

P(A and B) = 0.55 * 0.80 = 0.44

Therefore, the probability that Mark makes both goals is 0.44.