An insurer offers a health plan to the employees of a large company. As part of

Question

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 C are

StartFraction 17 Over 66 EndFraction1766,

StartFraction 19 Over 88 EndFraction1988,

and

StartFraction 7 Over 24 EndFraction724,

respectively. Determine the probability that a randomly chosen employee will choose no supplementary coverage.

Explanation / Answer

P(A)=17/66 ;P(B)+19/88 ;P(C)=7/24

from above as P(A) =P(AUB)+P(AUC)

hence 2*(P(AUBUC) =(17/66 +19/88+7/24)

P(AUBUC)=0.3826

probability that a randomly chosen employee will choose no supplementary coverage =1-P(AUBUC)

=1-0.3826=0.6174

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