(A) 0.04 (B) 0.16 (C) 0.20 D) 0.80 (E) 0.96 15. An insurer offers a health plan

Question

(A) 0.04 (B) 0.16 (C) 0.20 D) 0.80 (E) 0.96 15. An insurer offers a health plan to the employees of a large company. As part of this plan, the individual employees may choose exactly two of the supplementary coverages A, B, and C, or they may choose no supplementary coverage. The proportions of the company's employees that choose coverages A, B, and Care 1/4, 1/3, and 5/12 respectively. Calculate the probability that a randomly chosen employee will choose no supplementary coverage. (A) (B) 47/144 (D) 97/144 16. An insurance company determines that N, the number of claims received in a week, is a random variable with PlN nj where in 20. The company also determines that the number of claims received in a given week is independent of the number of claims received in any other week. Calculate the probability that exactly seven claims will be re ei, add, in

Explanation / Answer

here for they have two choose two or none

hence P(AnB)+P(AnC) =1/4

P(BnA)+P(BnC)=1/3

and P(CnA)+P(CnB)=5/12

solving theses (3) equations

2*P(AnB) = (1/4)+(1/3)-5/12 =2/12

P(AnB)=1/12

2*P(AnC)= 1/4+5/12-1/3 =4/12

P(AnC)=2/12

and 2* P(BnC) =1/3+5/12 -1/4 =6/12

P(BnC)=3/12

hence probabilty of no policy taken =1-(1/12)-(2/12)-3/12 =1/2

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