A baseball player has a batting average of 0.305. What is the probability that he has exactly 2 hits in his next 7 at bats? Round your answer to four decimal places.

The probability the baseball player has exactly 2 hits in his next 7 bats is .

This problem involves the binomial probability formula since we are dealing with a sequence of independent trials (each at-bat is independent), and the outcome for each trial is either a hit or no hit.

The binomial probability formula is:

\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
\]

Where:
- \(n = 7\) (number of at-bats)
- \(k = 2\) (number of hits)
- \(p = 0.305\) (probability of a hit)
- \(1 - p = 0.695\) (probability of no hit)

Now, we'll calculate this step by step.

1. The binomial coefficient \(\binom{n}{k}\) is calculated as:

\[
\binom{7}{2} = \frac{7!}{2!(7 - 2)!} = \frac{7 \times 6}{2 \times 1} = 21
\]

2. Now, we calculate the probability:

\[
P(X = 2) = 21 \times (0.305)^2 \times (0.695)^5
\]

Let me calculate this for you.The probability that the baseball player gets exactly 2 hits in his next 7 at-bats is \(0.3168\).

Do you have any questions or would you like more details on the steps?

Here are 5 related questions to expand on this:
1. What is the probability of the player getting exactly 3 hits in his next 7 at-bats?
2. How would the probability change if the player had a batting average of 0.400?
3. What is the probability of the player getting no hits in 7 at-bats?
4. What is the probability of getting at least 2 hits in 7 at-bats?
5. How many hits is the player expected to get in 7 at-bats?

**Tip:** In binomial probability, the mean number of successes can be found by multiplying the number of trials by the probability of success \( \mu = n \times p \).

A baseball player has a batting average of 0.305. What is the probability that he has exactly 2 hits in his next 7 at bats? Round your answer to four decimal places.

Learn how to calculate the probability that a baseball player with a batting average of 0.305 gets exactly 2 hits in his next 7 at-bats. This problem involves the binomial probability formula and is suitable for students in Grades 10-12.

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