Answer:
0.285/28.5%
Explanation:
The probability of a baseball player getting exactly 1 hit in his next 7 at-bats can be calculated using the binomial probability formula.
To use this formula, we need to know two things: the player's batting average and the number of at-bats he has had.
Given that the player has a batting average of 0.165, we can calculate the probability of getting a hit in a single at-bat as follows:
Probability of getting a hit = batting average = 0.165
Now, we can use the binomial probability formula, which is:
P(x) = nCx * p^x * q^(n-x)
Where:
- P(x) is the probability of getting exactly x hits
- nCx is the number of ways to choose x hits from n at-bats (calculated as n! / (x! * (n-x)!)
- p is the probability of getting a hit in a single at-bat
- q is the probability of not getting a hit in a single at-bat (1 - p)
- x is the number of hits we want to calculate the probability for
- n is the total number of at-bats
In this case, we want to calculate the probability of getting exactly 1 hit in 7 at-bats, so x = 1 and n = 7.
Let's plug in the values and calculate:
P(1) = 7C1 * (0.165)^1 * (1 - 0.165)^(7-1)
Using the binomial coefficient formula, 7C1 = 7! / (1! * (7-1)!) = 7.
P(1) = 7 * (0.165)^1 * (1 - 0.165)^(7-1)
P(1) = 7 * 0.165 * 0.835^6
Calculating this expression, we get:
P(1) ≈ 7 * 0.165 * 0.241
P(1) ≈ 0.285
Therefore, the probability that the baseball player will get exactly 1 hit in his next 7 at-bats is approximately 0.285 or 28.5%.