Do The Math Q6

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 14 , 13 and 512 respectively.

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

  1. 0
  2. 47144
  3. 12 Correct Answer
  4. 97144
  5. 79

Solution: C

A Venn diagram for this situation looks like:

We want to find

We have

Adding these three equations gives

Alternatively the three equations can be solved to give x = 1/12, y = 1/6, z =1/4 again leading to