Question

A family has three cars, with independent probability of claim during a year of 1/8, 1/10, and 1/20. What is the probability the family files an automobile claim in a given year?

Answer 1

The family is said to file an automobile claim if it files claim for any 1 car (OR) any two cars (OR) all 3 Cars.

So, the probability(P) the family files an automobile claim in a given year =[P(claiming any 1 car)] + [P(claiming any two cars)] + [P(claiming all 3 cars)] =[1/8 + 1/10 + 1/20] + [(1/8*1/10) + (1/8*1/20) + (1/10*1/20)] + [1/8*1/10*1/20] =0.275+0.02375+0.000625 =0.299375

[since claims of each car are independent, their probabilities can be multiplied to get joint probability. If A and B are independent, then P(AB) =P(A)*P(B)].