A fire insurance company has high-risk, medium-risk, and low-risk clients, that have, respectively, probabilities 0.02, 0.01, and 0.0025 of filing claims within a given year. The proportions of the numbers of clients in the three categories are 0.10, 0.20, and 0.70, respectively. What is the probability that a randomly selected filed claim came from a high-risk client?

Probability that the claim came from a high-risk client = claim from a high-risk client / claim from all clients

= 0.002 / (0.002 + 0.002 + 0.00175)

= 0.002 / 0.00575‬

= 0.3478

= 0.35

Step-by-step explanation:

Claims filed by each group of clients is gotten by multiplying the probabilities of occurrence by proportions of the number of client in the category

Claims filed by high-risk clients = 0.02 * 0.10 = 0.002‬

Claims filed by medium-risk clients = 0.01 * 0.20 = 0.002‬

Claims filed by low-risk clients = 0.0025 * 0.70 = 0.00175‬

The problem uses the perimeter formula.  P = 2w + 2l   where w is the width, and l is the length.

We know the length (l) is 3 inches longer than it's width (or l = w+3).  Substitute w +3 into Perimeter equation

P = 2w + 2(w+3).  That simplifies to P = 4w + 6.

Since P + 42,   we have 42 = 4w +6.  With some simple algebra we find that w = 9 and l = 12.

Hope this helps!