c15.9: A basketball player has made 80​% of his foul shots during the season. Assuming the shots are​ independent, find the probability that in​ tonight's game he does the following.

Question

A basketball player has made 80​% of his foul shots during the season. Assuming the shots are​ independent, find the probability that in​ tonight's game he does the following.

​a) Misses for the first time on his third attempt

​b) Makes his first basket on his fourth shot

​c) Makes his first basket on one of his first 3 shots

Answer 1

a) .8x.8x.2 =.128 = 12.8 %

b) .2x.2x.2x.8 = .0064 = 0.64% = < 1% chance

c) .8 chance on 1st shot

.2x.8 = .16 on 2nd shot

.2x.2x.8 = .032 on 3rd shot

sum them: .992 = 99.2% chance of getting a basket on one of the 1st 3 shots

or look at it another way. Just calculate the chance of not getting one shot in 3 trys: .2x.2x.2 = .008 = 0.8% chance of missing 3 times in a row. then subtract that from 100%. 100-.8 = 99.2% chance of getting at least one basket in 3 tries