Question

An insurance company divides its policyholders into low-risk and high-risk classes. 60% were in the low-risk class and 40% in the high-risk class. Of those in the low-risk class, 80% had no claims, 15% had one claim, and 5% had two claims. Of those in the high-risk class, 50% had no claims, 30% had one claim, and 20% had two claims. (Write answers as exact decimals.)
a) What is the probability that a randomly selected policyholder is high-risk and filed no claims?
b) What is the probability that a randomly selected policyholder filed two claims?

Answer 1

Answer:

a). 0.294

b) 0.11

Step-by-step explanation:

From the given information:

the probability of the low risk = 0.60

the probability of the high risk = 0.40

let $C_o$ represent no claim

let $C_1$ represent 1 claim

let $C_2$ represent 2 claim :

For low risk;

so, $C_o$  = (0.80 * 0.60 = 0.48),  $C_1$ =  (0.15* 0.60=0.09),   $C_2$ = (0.05 *  0.60=0.03)

For high risk:

$C_o$  = (0.50 *  0.40 = 0.2),  $C_1$ =  (0.30 *  0.40 = 0.12) ,   $C_2$ = ( 0.20 *  0.40 = 0.08)

Therefore:

a),  the probability that a randomly selected policyholder is high-risk and filed no claims can be computed as:

$P(H|C_o) = \dfrac{P(H \cap C_o)}{P(C_o)}$

$P(H|C_o) = \dfrac{(0.2)}{(0.48+0.2)}$

$P(H|C_o) = \dfrac{(0.2)}{(0.68)}$

$P(H|C_o) = 0.294$

b) What is the probability that a randomly selected policyholder filed two claims?

the probability that a randomly selected policyholder be filled with two claims = 0.03 + 0.08

= 0.11