SOLUTION: Lauren is the point guard on her basketball team. She estimates that her chances of getting a 3-pointer are 85% when there is no one defending against her, but only 60% when there

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Question 1033625: Lauren is the point guard on her basketball team. She estimates that her chances of getting a 3-pointer are 85% when there is no one defending against her, but only 60% when there is a defender. There is a 50% chance that the girl assigned to defend her will not be close enough to block the shot. What is the probability of Lauren scoring a 3-point shot?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.