Question

homework: section 4.3
score: 2/15 answered: 2/15
question 3
a baseball player has a batting average of 0.265. what is the probability that he has exactly 4 hits in his next 7 at bats? round your answer to four decimal places.
the probability the baseball player has exactly 4 hits in his next 7 bats is i
basic funcs trig

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 $p=0.265$ (probability of getting a hit in a single at - bat). Then $1 - p=1 - 0.265 = 0.735$.

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 $P(X = 4)$

$P(X = 4)=C(7,4)\times p^{4}\times(1 - p)^{7 - 4}=35\times(0.265)^{4}\times(0.735)^{3}$.
$(0.265)^{4}=0.265\times0.265\times0.265\times0.265\approx0.005006$
$(0.735)^{3}=0.735\times0.735\times0.735\approx0.393$.
$P(X = 4)=35\times0.005006\times0.393\approx0.0689$.

Answer:

$0.0689$