Question

Bill has a 12.105% chance of hitting a target when he shoots an arrow at it. Bill shot 21 arrows at a target and exactly 2 of them hit the target. What is the probability that the first two arrows hit the target?

Answer 1

The probability of Bill hitting the target with the first two arrows is approximately 1.465%, found by multiplying the individual probabilities of hitting the target with each arrow.

Step-by-step explanation:

The question asks for the probability that the first two arrows hit the target when Bill shot 21 arrows and exactly 2 of them hit the target, given that Bill has a 12.105% chance of hitting the target with each arrow. The events of hitting the target with each arrow are independent, meaning the outcome of one does not affect the other. Therefore, to calculate the probability of the first two arrows hitting the target, we multiply the probabilities of each event happening individually.

The probability of hitting the target with the first arrow is 0.12105. The same is true for the second arrow. Thus, the probability of hitting the target with both the first and second arrows is:
P(first hit) × P(second hit) = 0.12105 × 0.12105 = 0.0146532025.

The probability is approximately 1.465% that the first two arrows hit the target.