If the probability of a basketball player making a shot is 75%,

Question

If the probability of a basketball player making a shot is 75%, what is the probability that they will make a basket on at most 5 of the next 6 shots?

Answer 1

Hi Autumn, to solve this, use the binomial distribution. There are two ways to get to the answer.

 

Method 1:

Find the probability of 0, 1, 2, 3, 4, 5 baskets individually and add them up to get the total probability. This requires the use of the binomial distribution equation 6 times:

 

P(x'0) = 6!/(0! * (6-0)!)  * .75⁰ * .25⁶

P(x'1) = ...

...

P(x'5) = ...

 

Then once all of the individual probabilities are known, just add them up to get the final probability.

 

Method 2:

 

P(x ≤ 5) = 1 - P(x'6)

 

Doing it this way means we only have to use the binomial distribution 1 time to get to the answer.

 

P(x ≤ 5) = 1 - ((6!/(6! * (6 - 6)!)) * .75⁶ * .25⁰⁾

 

Questions?

Answer 2

what you want is 1 - P(all six shots are missed) and that is (1 - 0.25⁶), assuming that all shorts are of a comparable type and distance, and that this P(miss) = 0.25 can be treated as constant.