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.