An insurance company insures a good driver and a bad driver on the same policy.

Question

An insurance company insures a good driver and a bad driver on the same policy. The table below gives the probability of a given number of claims occurring for each of these drivers in the next ten years. 4 Number of claims Probability for the good driver 0.50 0.35 0.15 0.00 Probability for the bad driver 0.20 0.30 0.40 0.10 1 2 The number of claims occurring for the two drivers are independent. Calculate the mode of the distribution of the total number of claims occurring on this policy in the next ten years

Explanation / Answer

Assuming that the distribution of the number of good and

number of bad drivers are independent in the population, we

have, P(X = 0) = 0.50 + 0.20 - (0.50 * 0.20) = 0.6.&

P(X = 1) = 0.35 + 0.30 - (0.35 * 0.30) = 0.545.

P(X = 2) = 0.15 + 0.40 - (0.15 * 0.4) = 0.49.

P(X = 3) = 0.00 + 0.10 - (0.00 * 0.10) = 0.10.

Hence, P(X = 0) > P(X = 1) > P(X = 2) > P(X = 3)

Hence, the mode of the distribution of total nunber of claims

= 0. (Ans).

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