a baseball player has a hitting average of 0.325. if seven at - bats are randomly selected, what is the probability of getting 4 hits?
0.01
0.02
0.08
0.12

Question

Accepted Answer

# 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), $p=0.325$, and $1 - p = 1-0.325 = 0.675$

## Step3: Calculate the combination $C(n,k)$
$$
\begin{align*}
C(7,4)&=\frac{7!}{4!(7 - 4)!}\
&=\frac{7!}{4!3!}\
&=\frac{7\times6\times5\times4!}{4!\times3\times2\times 1}\
&=35
\end{align*}
$$

## Step4: Calculate $p^{k}$ and $(1 - p)^{n - k}$
$p^{k}=(0.325)^{4}\approx0.01139$
$(1 - p)^{n - k}=(0.675)^{3}\approx0.30755$

## Step5: Calculate the probability $P(X = 4)$
$$
\begin{align*}
P(X = 4)&=C(7,4)\times p^{4}\times(1 - p)^{3}\
&=35\times0.01139\times0.30755\
&\approx35\times0.00350\
&\approx0.12
\end{align*}
$$

# Answer:
0.12

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the binomial probability formula

Step2: Determine the values of \(n\), \(k\), and \(p\)

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

Step4: Calculate \(p^{k}\) and \((1 - p)^{n - k}\)

Step5: Calculate the probability \(P(X = 4)\)

Answer: