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The problem shown in the image asks:  
"A baseball player has a batting average of 0.35. What is the probability that he has exactly 2 hits in his next 7 at bats?"

This is a binomial probability problem because:
- Each at-bat is an independent trial.
- The probability of success (getting a hit) is 0.35.
- The number of trials (at-bats) is 7.
- We are looking for the probability of exactly 2 successes (hits) out of 7 at-bats.

The binomial probability formula is:

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

Where:
- \( P(X = k) \) is the probability of getting exactly \( k \) successes,
- \( n \) is the number of trials (in this case, 7),
- \( k \) is the number of successes (in this case, 2),
- \( p \) is the probability of success on each trial (0.35 here), and
- \( \binom{n}{k} \) is the binomial coefficient, representing the number of ways to choose \( k \) successes from \( n \) trials.

Let's calculate this step-by-step. I'll compute it for you now.The probability that the baseball player will get exactly 2 hits in his next 7 at-bats is approximately **0.298** or 29.8%.

Do you need further details or explanations on this? Here are 5 related questions for deeper understanding:

1. How would the probability change if the player had a higher batting average?
2. What is the probability of getting at least 2 hits in 7 at-bats?
3. Can the binomial distribution be used for continuous data, or is it strictly for discrete outcomes?
4. What is the expected number of hits in 7 at-bats with this batting average?
5. How does the variance of the number of hits relate to the number of trials and probability of success?

**Tip:** The binomial distribution assumes each trial is independent, meaning the outcome of one at-bat does not affect the outcome of another.

A baseball player has a batting average of 0.35. What is the probability that he has exactly 2 hits in his next 7 at bats?

Explore the solution to the probability problem of a baseball player with a batting average of 0.35, calculating the likelihood of getting exactly 2 hits in 7 at-bats. This problem applies binomial distribution concepts and is suitable for advanced high school students and undergraduates.

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