- A large company offers its employees 2 different health insurance plans and 2 different life...

- A large company offers its employees 2 different health insurance plans and 2 different life insurance plans. The table below shows the proportions of employees who choose these plans. Since it is known that a randomly selected employee chooses Plan 2 in life insurance, what is the probability of choosing Plan 1 in health insurance?
Life insurance
Health Insurance 1. Plan 2. Plan
1. Plan 20% 15%
2. Plan 25% 40%

Expert Solution

The table gives us joint distribution.

Thus, Probability that an employee has Plan 1 in life insurance and plan 1 in health insurance is 0.2

Probability that an employee has Plan 1 in life insurance and plan 2 in health insurance is 0.25

Probability that an employee has Plan 2 in life insurance and plan 1 in health insurance is 0.15

Probability that an employee has Plan 2 in life insurance and plan 2 in health insurance is 0.40

From this joint distribution, we can find the marginal distribution.

Thus, Probability that an employee has Plan 1 in life insurance is 0.45

Probability that an employee has Plan 2 in life insurance is 0.55

Probability that an employee has Plan 1 in health insurance is 0.35

Probability that an employee has Plan 2 in health insurance is 0.65

We want Probability that employee chooses plan 1 in health insurance given he has plan 2 in life insurance.

Thus, Probability that employee chooses plan 1 in health insurance given he has plan 2 in life insurance is 0.27273

orchestra answered 1 year ago

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