Respuesta :
Answer:
64% probability that BSU win this game
Step-by-step explanation:
For each free throw, there are only two possible outcomes. Either he makes it, or he does not. The probability of 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.
Two free throws.
This means that [tex]n = 2[/tex]
A player in Boise State University basketball team makes 80% of his free throws.
This means that [tex]p = 0.8[/tex]
What is the probability that BSU win this game
The team is trailing by 1 and he will attemp 2 free throws. If he makes both, BSU wins the game.
So we have to find P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.8)^{2}.(0.2)^{0} = 0.64[/tex]
64% probability that BSU win this game
