a baseball player has a hitting average of 0.325. if seven at - bats are randomly selected, what is the…

Answer:

0.08

Explanation:

Step1: Identify the binomial - probability formula

The binomial - probability formula is $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success on a single trial, and $C(n,k)=\frac{n!}{k!(n - k)!}$.

Step2: Determine the values of $n$, $k$, and $p$

Here, $n = 7$ (number of at - bats), $k = 4$ (number of hits), and $p=0.325$ (hitting average). Then $1 - p = 1-0.325 = 0.675$.

Step3: Calculate the combination $C(n,k)$

$C(7,4)=\frac{7!}{4!(7 - 4)!}=\frac{7!}{4!3!}=\frac{7\times6\times5}{3\times2\times1}=35$.

Step4: Calculate the probability $P(X = 4)$

$P(X = 4)=C(7,4)\times p^{4}\times(1 - p)^{7 - 4}=35\times(0.325)^{4}\times(0.675)^{3}$. $(0.325)^{4}=0.325\times0.325\times0.325\times0.325\approx0.01139$. $(0.675)^{3}=0.675\times0.675\times0.675\approx0.30755$. $P(X = 4)=35\times0.01139\times0.30755\approx0.08$.