Respuesta :
Answer:
There is a 34.3% probability that he makes all of the shots.
Step-by-step explanation:
For each foul shot that he takes during the game, there are only two possible outcomes. Either he makes it, or he misses. This means that we use the binomial probability distribution to solve this problem.
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 combinatios 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.
In this problem we have that:
[tex]n = 3, p = 0.7[/tex]
What is the probability that he makes all of the shots?
This is P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.7)^{3}.(0.3)^{0} = 0.343[/tex]
There is a 34.3% probability that he makes all of the shots.
The probability that the basketball player makes all of the shots is 0.343.
How to calculate probability?
From the information given, the basketball player has made 70% of his foul shots during the season.
When he he shoots 3 foul shots in tonight's game, the probability that he makes all of the shots will be:
= (70%)³
= 0.7³
= 0.343
In conclusion, the correct option is 0.343.
Learn more about probability on:
https://brainly.com/question/25870256
