A baseball player's batting average is 0.341, which can be interpreted as the probability that he got a hit each time at bat. Thus, the probability that he did not get a hit is 1-0.341 = 0.659. Assume that the occurrence of a hit in any given at-bat has no effect on the probability of a hit in other at-bats. In one game, the player had 4 at-bats. What is the probability that he had 2 hits? What expression can be used to calculate the probability? O A. OB. (2) (3) (2) O C. 4 O D. 4 (0.341) (0.659)4 2 (0.341) (0.659)2 (0.341 +0.659)² (0.341 +0 (0.341)²(0.659)² The probability that the player had 2 hits in 4 at-bats is (Round to three decimal places as needed.)
A baseball player's batting average is 0.341, which can be interpreted as the probability that he got a hit each time at bat. Thus, the probability that he did not get a hit is 1-0.341 = 0.659. Assume that the occurrence of a hit in any given at-bat has no effect on the probability of a hit in other at-bats. In one game, the player had 4 at-bats. What is the probability that he had 2 hits? What expression can be used to calculate the probability? O A. OB. (2) (3) (2) O C. 4 O D. 4 (0.341) (0.659)4 2 (0.341) (0.659)2 (0.341 +0.659)² (0.341 +0 (0.341)²(0.659)² The probability that the player had 2 hits in 4 at-bats is (Round to three decimal places as needed.)
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![**Title: Calculating Probability of a Baseball Player's Hits Using Batting Average**
**Introduction:**
In baseball, a player's batting average (BA) is a key statistic that represents the likelihood of hitting the ball successfully during an at-bat. This concept can be applied to calculate the probability of specific outcomes in a series of at-bats.
**Problem Statement:**
A baseball player’s batting average is 0.341, which can be interpreted as the probability that he got a hit each time at bat. Thus, the probability that he did not get a hit is 1 - 0.341 = 0.659. Assume that the occurrence of a hit in any given at-bat has no effect on the probability of a hit in other at-bats. In one game, the player had 4 at-bats. What is the probability that he had 2 hits?
**Question:**
What expression can be used to calculate the probability?
**Options:**
A.
\[
\left( \begin{array}{c}
6 \\
4 \\
\end{array} \right) (0.341)^{4} (0.659)^{4}
\]
B.
\[
\left( \begin{array}{c}
4 \\
2 \\
\end{array} \right) (0.341)^4 (0.659)^{2}
\]
C.
\[
\left( \begin{array}{c}
4 \\
2 \\
\end{array} \right) (0.341 + 0.659)^{2}
\]
D.
\[
\left( \begin{array}{c}
4 \\
2 \\
\end{array} \right) (0.341)^2 (0.659)^2
\]
**Answer Calculation Box:**
The probability that the player had 2 hits in 4 at-bats is \( \boxed{} \).
(Round to three decimal places as needed.)
**Explanation of Terms and Calculation:**
1. **Combination Calculation:**
\[
\left( \begin{array}{c}
n \\
k \\
\end{array} \right)
\]
is the binomial coefficient, representing the number of ways to choose \( k \) successes (hits) out of \( n \) trials (at-bats).
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff138e77-4b21-4b3f-a581-600ea0faba85%2F0e097c15-9665-4e51-a06c-6fafe07eae13%2F8x5ilnp_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Probability of a Baseball Player's Hits Using Batting Average**
**Introduction:**
In baseball, a player's batting average (BA) is a key statistic that represents the likelihood of hitting the ball successfully during an at-bat. This concept can be applied to calculate the probability of specific outcomes in a series of at-bats.
**Problem Statement:**
A baseball player’s batting average is 0.341, which can be interpreted as the probability that he got a hit each time at bat. Thus, the probability that he did not get a hit is 1 - 0.341 = 0.659. Assume that the occurrence of a hit in any given at-bat has no effect on the probability of a hit in other at-bats. In one game, the player had 4 at-bats. What is the probability that he had 2 hits?
**Question:**
What expression can be used to calculate the probability?
**Options:**
A.
\[
\left( \begin{array}{c}
6 \\
4 \\
\end{array} \right) (0.341)^{4} (0.659)^{4}
\]
B.
\[
\left( \begin{array}{c}
4 \\
2 \\
\end{array} \right) (0.341)^4 (0.659)^{2}
\]
C.
\[
\left( \begin{array}{c}
4 \\
2 \\
\end{array} \right) (0.341 + 0.659)^{2}
\]
D.
\[
\left( \begin{array}{c}
4 \\
2 \\
\end{array} \right) (0.341)^2 (0.659)^2
\]
**Answer Calculation Box:**
The probability that the player had 2 hits in 4 at-bats is \( \boxed{} \).
(Round to three decimal places as needed.)
**Explanation of Terms and Calculation:**
1. **Combination Calculation:**
\[
\left( \begin{array}{c}
n \\
k \\
\end{array} \right)
\]
is the binomial coefficient, representing the number of ways to choose \( k \) successes (hits) out of \( n \) trials (at-bats).
2
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