Question

A portfolio of claims contains 10 each of bodily injury, property damage, worker's compensation and comprehensive claims. Five claims are randomly drawn from this portfolio. Find the probability that the selected claims contain exactly three claims from one coverage and exactly two claims from one of the other coverages.

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Number of types of coverages = 4

Number of claims in each type = 10

Total number of coverages = 4x10 = 40

Number of coverages to be selected = 5

P(the selected claims contain exactly three claims from one coverage and exactly two claims from one of the other coverage) = Number of ways to select any two coverages from the 4 types (order is important because we select 3 coverages from the first and 2 coverages from second) x Number of ways to select 3 coverages from 10 x Number of ways to select 2 coverages from 10 / Number of ways to select 5 coverages from total 40

= 4P2 x 10C3 x 10C2 / 40C5

= 12 x 120 x 45 / 658,008

= 0.09848