Question

A basketball player is historically an 82% free throw shooter. If she attempts 10 free throws, what is the probability she makes at least 8 of them? (Round to three decimal places)

options for answers
1. 0.737
2. 0.820
3. 0.561
4. 0.296

please show how you figure it out that way i know for future reference.

Answer 1

1. 0.737

Explanation:

For each free throw, there are only two possible outcomes. Either the player makes it, or he does not. The probability of the player making a free throw is independent of other free throws. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

A basketball player is historically an 82% free throw shooter.

This means that
`p = 0.82`

She attempts 10 free throws

This means that
`n = 10`

What is the probability she makes at least 8 of them?

`P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)`

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 8) = C_(10,8).(0.82)^(8).(0.18)^(2) = 0.298`

`P(X = 9) = C_(10,9).(0.82)^(9).(0.18)^(1) = 0.302`

`P(X = 10) = C_(10,10).(0.82)^(10).(0.18)^(0) = 0.137`

`P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.298 + 0.302 + 0.137 = 0.737`