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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?

Respuesta :

ajeigbeibraheem

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 [tex]C_o[/tex] represent no claim

let [tex]C_1[/tex] represent 1 claim

let [tex]C_2[/tex] represent 2 claim :

For low risk;

so, [tex]C_o[/tex]  = (0.80 * 0.60 = 0.48),  [tex]C_1[/tex] =  (0.15* 0.60=0.09),   [tex]C_2[/tex] = (0.05 *  0.60=0.03)

For high risk:

[tex]C_o[/tex]  = (0.50 *  0.40 = 0.2),  [tex]C_1[/tex] =  (0.30 *  0.40 = 0.12) ,   [tex]C_2[/tex] = ( 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:

[tex]P(H|C_o) = \dfrac{P(H \cap C_o)}{P(C_o)}[/tex]

[tex]P(H|C_o) = \dfrac{(0.2)}{(0.48+0.2)}[/tex]

[tex]P(H|C_o) = \dfrac{(0.2)}{(0.68)}[/tex]

[tex]P(H|C_o) = 0.294[/tex]

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

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