Pro basketball player Shaquille O’Neal is a poor free-throw shooter. Consider situations in which he shoots a pair of free throws. The probability that he makes the first free throw is 0.50. Given that he makes the first, suppose the probability that he makes the second is 0.60. Given that he misses the first, suppose the probability that he makes the second one is 0.40.
a. What is the probability that he makes both free throws?
b. Find the probability that he makes one of the two free throws (i) using the multiplicative rule with the two possible ways he can do this and (ii) by defining this as the complement of making neither or both of the free throws.
c. Are the results of the free throws independent? Explain.