MATH SOLVE

2 months ago

Q:
# Suppose the probability that a softball player gets a hit in any single at-bat is .300. assuming that her chance of getting a hit is independent, what is the probability that she will get her first hit on her fourth at-bat (attempt) in a game?

Accepted Solution

A:

Answer: 0.1029 ≈ 0.10

Explanation:

1) Since the probabilities of batting a hit are independent of what happened the previous attempts, the joint probability is the product of the individual probabilities.

2) The probability she gets her first hit on her fourth attempt at-bat is the probability that she does not bat a hit on her first three attempts and bat a hit on her fourth attempt.

3) The probability of not batting a hit on each attempt is 1 - the probability of batting a hit, which is 1 - 0.300 = 0.700.

4) So, the joint probability will be: 0.700 × 0.700 × 0.700 × 0.300 = 0.1029 ≈ 0.10

Explanation:

1) Since the probabilities of batting a hit are independent of what happened the previous attempts, the joint probability is the product of the individual probabilities.

2) The probability she gets her first hit on her fourth attempt at-bat is the probability that she does not bat a hit on her first three attempts and bat a hit on her fourth attempt.

3) The probability of not batting a hit on each attempt is 1 - the probability of batting a hit, which is 1 - 0.300 = 0.700.

4) So, the joint probability will be: 0.700 × 0.700 × 0.700 × 0.300 = 0.1029 ≈ 0.10