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!