Joe's batting average is .323. (That is, he averages 0.323 hits per at bat.) What is the probability that he will get three hits in three at-bats? Express your answer as a decimal to the nearest hundredth.

USERSPPB Oct 7, 2023

#1**0 **

To find the probability that Joe will get three hits in three 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 (at-bats in this case), which is 3.

k is the number of successful outcomes (hits in this case), which is also 3.

p is the probability of success on a single trial (Joe's batting average), which is 0.323.

(n choose k) represents the binomial coefficient, which is calculated as n! / (k!(n - k)!).

Let's calculate it step by step:

Calculate (n choose k): (3 choose 3) = 3! / (3!(3 - 3)!) = 1

Calculate p^k: 0.323^3 ≈ 0.033857

Calculate (1 - p)^(n - k): (1 - 0.323)^(3 - 3) = 0.677911

Now, plug these values into the formula:

P(X = 3) = 1 * 0.033857 * 0.677911 ≈ 0.02299

So, the probability that Joe will get three hits in three at-bats is approximately 0.023, rounded to the nearest hundredth.

bingboy Oct 7, 2023