Question 1010686: Suppose that the probability of your favorite baseball player getting a hit at bat is 0.45. Assume that each at bat is independent. What is the probability that he bats eight times and gets exactly four hits? (Round to 4 decimal places.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
p(x) = c(n,x) * p^x * q^(n-x)
p(x) is the probability of getting exactly x h9its.
c(n,x) is the combination formula of n! / (x! * (n-x)!).
it tells you how many ways you can get x things out of n where order doesn't matter.
p is the probability of success, in this case the probability of getting a hit.
q is the probability of failure, in this case the probability of not getting a hit.
in this formula, q is always equal to 1-p.
x is the number of things you want to choose out of n things.
n is the total number of things you are choosing from.
in your problem, the formula of p(x) = c(n,x) * p^x * q^(n-x) becomes:
p(4) = c(8,4) * .45^4 * .55^4 = .2627 = 26.27%
the total probability is 1 , as it should be.
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