Question

a man aiming at a target receives 10 points if his shot is within 1 inch of the target, 5 points if it is between 1 and 3 inches of the target, and 3 points if it is between 3 and 5 inches of the target. find the expected number of points scored if the distance from the shot to the target is uniformly distributed between 0 and 10.

Answer 1

To find the expected number of points scored, calculate the probabilities of each score and multiply by corresponding points. The expected number of points is 2.6.

Step-by-step explanation:

To find the expected number of points scored, we need to calculate the probability of each score and then multiply it by the corresponding points. Let's break it down:

1. The probability of getting a score of 10 is the probability that the shot is within 1 inch of the target, which is (1/10) = 0.1.
2. The probability of getting a score of 5 is the probability that the shot is between 1 and 3 inches of the target, which is (3-1)/(10-0) = 0.2.
3. The probability of getting a score of 3 is the probability that the shot is between 3 and 5 inches of the target, which is (5-3)/(10-0) = 0.2.

Now, we can calculate the expected number of points:

Expected points = (Probability of score 10 * Points for score 10) + (Probability of score 5 * Points for score 5) + (Probability of score 3 * Points for score 3)

Expected points = (0.1 * 10) + (0.2 * 5) + (0.2 * 3) = 1 + 1 + 0.6 = 2.6