Final answer:
The probability that Barry Bonds hits his next home run on the fifth at-bat is calculated by multiplying the probability of not hitting a home run in the first four at-bats (0.84 each) with the probability of hitting it on the fifth (0.16), which is option d) 0.057.
Step-by-step explanation:
The student's question is about calculating the probability that Barry Bonds hits a home run on his fifth at-bat given that the individual at-bats are independent and that the probability of hitting a home run on any given at-bat is 0.16. To find the probability of hitting the first home run on the fifth at-bat specifically, we must consider that Bonds does not hit a home run in the first four at-bats and does hit one on the fifth. This scenario can be computed as the product of the probabilities of not hitting a home run in each of the first four at-bats (0.84 each) and the probability of hitting a home run on the fifth at-bat (0.16).
So the calculation is as follows:
- Probability of not hitting a home run: 1 - 0.16 = 0.84
- Probability of not hitting a home run in the first four at-bats: 0.84 ^ 4
- Probability of hitting a home run on the fifth at-bat: 0.16
- Total probability: (0.84 ^ 4) × 0.16
The computation is (0.84 ^ 4) × 0.16 = 0.057.
Therefore, the correct answer is option d) 0.057.