A pro basketball player is a poor free-throw shooter. Consider situations in whi

Question

A pro basketball player 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 0.48. Given that he makes the first, suppose the probability that he makes the second is 0.57. Given that he misses the first, suppose the probability that he makes the second one is 0.36.

Find the probability that he makes one of the two free throws using the multiplicative rule with the two possible ways he can do this.(please show clear detailed work,thanks)

Explanation / Answer

Ans:P(making first throw)=0.48

P(not making first throw)=1-0.48=0.52

P(making 2nd throw/makes first throw)=0.57

P(making 2nd throw/not makes first throw)=0.36

P(making 2nd throw/makes first throw)=0.57=P(making first and second throw)/P(making first throw)

P(making first and second throw)=0.57*0.48

P(making 2nd throw/not makes first throw)=0.36=P(not making first and making second throw)/P(not making first throw)

P(not making first and making second throw)=0.36*0.52

P(making second throw)=P(making first and second throw)+P(not making first and making second throw)

=0.57*0.48+0.36*0.52=0.46

P(making first or second)=P(making first)+P(making second)-P(making first and second)

=0.48+0.46-0.57*0.48=

0.48+0.46-0.27=0.67

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