A basketball player makes 60% of the free throws that he attempts, except that if he has just tried and missed a free throw then his chances of making a second one go down to only 30%. Suppose he has just been awarded two free throws.

Question

Find the probability that he makes both.
Find the probability that he makes at least one. (A tree diagram could help.)

Answer 1

Cannot draw tree diagram here.

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

"at least" = one or both

P(both) = .6 * .6

P(only second) = .4 * .3

P(only first) = .6 * .7

Either-or probabilities are found by adding the individual probabilities. Add the three probabilities.