Question 1033625
the way i see this problem is as follows:


she has 85% probability to score the 3 pointer if the defender is not close enough to give her a hard time.


she has 60% probability to score the 3 pointer if the defender is close enough to give her a hard time.


the defender has 50% probability to be close enough to give her a hard time.


the probability that she will make the shot is therefore .5 * .85 + .5 * .60 = .725.


she will be able to score the 3 pointer 72.5% of the time overall.


for example:


assume she tries 1000 times.


500 of those times the defender is close enough.
500 of those times the defender is not close enough.


for the 500 of the times that the defender is close enough, she scores .60 * 500 = 300 times.


for the 500 of the times that the defender is not close enough, she scores .85 * 500 = 425 times.


for the 1000 times that she tries, she scores 300 + 425 = 725 times.


725 / 1000 = .725 which is the probability we originally calculated above.