Respuesta :
Answer:
Option B) 0.435
Step-by-step explanation:
We are given the following information:
We treat player makes a shot as a success.
P(player makes a shot) = 39% = 0.39
Then the number of shots follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 3
We have to evaluate:
[tex]P(x =1)\\= \binom{3}{1}(0.39)^1(1-0.39)^2\\= 0.435[/tex]
0.435 is the probability that she makes 1 shot.
Option B) 0.435
The required probability that she makes 1 shot is 0.435.
Given that,
A basketball player makes 39% of her shots from the free throw line.
Suppose that each of her shots can be considered independent and that she throws 3 shots.
We have to find,
What is the probability that she makes 1 shot.
According to the question,
For each throw, the player either makes it or misses it. The probability of making each throw is the same, independent of other throws, thus, the binomial distribution is used to solve this question.
Binomial probability distribution:
Let X = the number of shots that he makes,
The binomial probability is the probability of exactly x successes on n repeated trials, with X having two possible outcomes.
[tex]P (X=x) = C_n,_x \ p^x \ (1-p)^{(n-x)}[/tex]
Where, [tex]^nc_x[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]^nc_x = \dfrac{n!}{x1(n-x)!}[/tex]
And p is the probability of a success on a single trial. makes 39% = 0.39 of the shots, 3 shots .
The probability of making all of them is P(X = 1),
Therefore,
[tex]P(X=1) = \ ^3C_1 . (0.39)^1. (1-0.39)^{2} \\\\P(X=1) = 3 \times 0.39 \times (0.61)^2\\\\P(X=1) = 0.435[/tex]
Hence, The required probability that she makes 1 shot is 0.435.
To know more about probability click the link given below.
https://brainly.com/question/8896407
