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,
[tex]\text{The probability of hitting 4 balls in 7 hit }^nC_r\times(p)^r\times(q)^{n-r}[/tex]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,
[tex]\begin{gathered} \text{The probability of hitting 4 balls in 7 hit =}\frac{7!}{4!}\times(0.165)^4\times(1-0.165)^{7-4} \\ =\text{35}\times(0.165)^4\times(0.835)^3 \\ =0.015 \end{gathered}[/tex]Hence, the probability of hitting 4 balls out of 7 is 0.015.
