Question

In the past, Ben has been able to hit a baseball at the batting cage 20% of the time. He decides to head back to the batting cage. What is the probability that his first hit will be on the eighth pitch? Round your answer to the nearest ten-thousandth.

Answer 1

The probability that Ben's first hit will be on the eighth pitch is approximately 0.0419.

Step-by-step explanation:

To find the probability that Ben's first hit will be on the eighth pitch, we need to calculate the probability of him not hitting the ball in the first seven pitches and then hitting it on the eighth pitch.

The probability of him not hitting the ball in a single pitch is 1 - 0.20 = 0.80.

Since each pitch is independent, the probability of him not hitting the ball in the first seven pitches is (0.80)^7 = 0.2097152.

Therefore, the probability of his first hit being on the eighth pitch is 0.2097152 * 0.20 = 0.0419430 (rounded to the nearest ten-thousandth).

Answer 2

The probability is 0.336.

To solve this, we need Binomial Probability equation for Repeated Trials.

P = nCr (p)^r (q)^(n-r)
where P = probability (unknown)
n = number of trials (8)
r = number of successes (1)
p = probability of success (.20)
q = probability of failure (0.80)

P = 8C1 (.20)^1 (.80)^7
= 0.336