Question

A baseball player has a batting average of 0.25. What is the probability that he has exactly 2 hits in his next 7 at bats

Answer 1

The probability that he has exactly 2 hits in his next 7 at-bats is 0.3115.

Explanation:

We are given that a baseball player has a batting average of 0.25 and we have to find the probability that he has exactly 2 hits in his next 7 at-bats.

Let X = Number of hits made by a baseball player

The above situation can be represented through binomial distribution;

`P(X = r) = \binom{n}{r}* p^(r) * (1-p)^(n-r); x = 0,1,2,......`

where, n = number of trials (samples) taken = 7 at-bats

r = number of success = exactly 2 hits

p = probability of success which in our question is batting average

of a baseball player, i.e; p = 0.25

SO, X ~ Binom(n = 7, p = 0.25)

Now, the probability that he has exactly 2 hits in his next 7 at-bats is given by = P(X = 2)

P(X = 2) =
`\binom{7}{2}* 0.25^(2) * (1-0.25)^(7-2)`

=
`21 * 0.25^(2) * 0.75^(5)`

= 0.3115