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A baseball player has a batting average of 0.15. What is the probability that he has exactly 7 hits in his next 7 at bats? Round your answer to four decimal places.

The probability the baseball player has exactly 7 hits in his next 7 bats is ______
I have an exam tomorrow and really want to know how to solve it step by step!

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Answer:

Explanation:

To find the probability that the baseball player has exactly 7 hits in his next 7 at-bats, we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Where:

- P(X = k) is the probability of getting exactly k hits.

- n is the number of trials (in this case, 7 at-bats).

- k is the number of successful trials (in this case, 7 hits).

- p is the probability of success in a single trial (batting average).

In this case, the player's batting average is 0.15, which means the probability of getting a hit in a single at-bat (p) is 0.15. So, we can calculate as follows:

P(X = 7) = (7 choose 7) * 0.15^7 * (1 - 0.15)^(7 - 7)

Using combinations: (7 choose 7) = 1 because there's only one way to get exactly 7 hits in 7 at-bats.

P(X = 7) = 1 * 0.15^7 * 0.85^0

P(X = 7) = 0.15^7

Now, calculate this probability:

P(X = 7) ≈ 0.000011390625

So, the probability that the baseball player has exactly 7 hits in his next 7 at-bats is approximately 0.00001139 (rounded to four decimal places). Good luck with your exam!

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