Respuesta :
Answer:
1. 0.737
Step-by-step 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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A basketball player is historically an 82% free throw shooter.
This means that [tex]p = 0.82[/tex]
She attempts 10 free throws
This means that [tex]n = 10[/tex]
What is the probability she makes at least 8 of them?
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.82)^{8}.(0.18)^{2} = 0.298[/tex]
[tex]P(X = 9) = C_{10,9}.(0.82)^{9}.(0.18)^{1} = 0.302[/tex]
[tex]P(X = 10) = C_{10,10}.(0.82)^{10}.(0.18)^{0} = 0.137[/tex]
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.298 + 0.302 + 0.137 = 0.737[/tex]
