Pro basketball player Shaquille ONeal is a poor freethrow sh

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 0.5. 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 exactly one of the two free throws.

c. Are the results of the free throws independent? Explain.

Solution

Let

A = makes first
B = makes second

a) Thus,

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

= 0.5 (0.60)

= 0.30 [answer]

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b)

P(exactly 1) = P(not A and B) + P(A and not B)

= P(not A) P(B|not A) + P(A) P(not B|A)

= 0.5 (0.40) + 0.5 (1-0.60)

= 0.40 [answer]

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c)

No. As you can see, the probability of making the second depends on making the first one.