Question

A baseball player has a batting average of 0.165. What is the probability that he has exactly 4 hits in his next 7 at bats?

Answer 1

Given,

A baseball player has a batting average of 0.165.

The probability of hitting the ball is 0.165.

The probability of hitting 4 balls in next 7 balls.

By using the binomial thorem,

`\text{The probability of hitting 4 balls in 7 hit }^nC_r*(p)^r*(q)^(n-r)`

Where, n is the number of total balls.

r is the number of hit.

p is the probability of hitting.

q is the probability of not hitting.

Substituting the values then,

`\begin{gathered} \text{The probability of hitting 4 balls in 7 hit =}(7!)/(4!)*(0.165)^4*(1-0.165)^(7-4) \\ =\text{35}*(0.165)^4*(0.835)^3 \\ =0.015 \end{gathered}`

Hence, the probability of hitting 4 balls out of 7 is 0.015.