Question

A professional organization sells term life insurance and major medical insurance. Of those who have just life insurance, 60% will renew next year, and 85% of those with only a major medical policy will renew next year. However, 90% of policyholders who have both types of policy will renew at least one of them next year. Of the policy holders, 65% have term life insurance, 55% have major medical, and 20% have both.
a. Calculate the percentage of policyholders that will renew at least one policy next year.
b. If a randomly selected policy holder does in fact renew next year, what is the probability that he or she has both life and major medical insurance?

Answer 1

Answer:

The answer is "0.765 and 0.2353".

Step-by-step explanation:

Please find the complete question in the attached file.

In point a:

P(a substantive term only)$=0.75-0.2 =0.55$

P(major health insurance only) $= 0.45-0.20=0.25$

P(both)$= 0.20$

P(renewal) =P(insurance and renewal term only)+P (substantial and renewable health insurance only)+P (both and renew)

$=0.55\times 0.7+0.25 \times 0.8+0.2 \times 0.9 \\\\ =0.765$

In point b:

In reality, the probability of having both life and major medical insurance provided the policyholder would renew next year

$= \frac{\text{P(both and renew)}}{\text{P(renew)}}$

$=\frac{0.2\times 0.9}{0.765}\\\\=0.2353$