QUESTION 1 You work at an organization that offers health care policies. The com

Question

QUESTION 1 You work at an organization that offers health care policies. The company first checks all applicants to see if they are cligible for any govemment programs and then offers advice on which policy/program is most beneficial to them (government and/or private). Given the following information, draw a joint probability table. Enter all answers on this exam using 4 decimal places with a 0 leading the decimal. All probabilities are independent. Variables are type of policy and level of coverage. Your company considers the type of policy, Customers are rated as eligible for Medicaid 30%), Patient Protection and Affordable care Act (PP ACA, 20% or private polices based on their income and or disability. You tf en sell these policies based on the level of everage that the person is interested in: Minimal coverage catastrophic only with a high co-pay (30%); Medium coverage with a moderate co-pay (40%); and full coverage-includes elective co-pay and psychiatric coverage with a small 1. What is the probability of a customer being interested in full coverage? QUESTION 2 2. What is the probability of being a customer who s wanting Full coverage and eligible for Medicaid? (Put answer in probabilities, not percents Click Save and Submit to save and submit. Click Save All Answers to save all answers. 16

Explanation / Answer

Define the Random variables

X : type of policy

X1: Customers are rated as eligible for medicaid , P(X1) =0.30

X2: Customers are are rated as Patient protection and affordable care act , P(X2) = 0.20

X3: Customers are rated as private policies based on their incomes

Since Total probability is one

P(X3) =1-(0.30+0.20) =0.50

Y : Level of coverage

Y1: Minimum coverage, P(Y1) = 0.30

Y2: Medium coverage , P(Y2) = 0.40

Y3: Full Coverage

since total probability is one

P(Y3) =1-( 0.40 +0.30) =0.30

Let X and Y are Independent

Hence P(X,Y) =P(X,Y)

The joint probability table of (X,Y)

a) P(customered being interested in full coverage) = P(Y3) = 0.3000

b) P(customer who is wanting the full coverage and eligible for medicaid) = P(X1,Y3) = 0.0900

X Total X1 X2 X3 Y Y1 0.12 0.08 0.2 0.4 Y2 0.09 0.06 0.15 0.3 Y3 0.09 0.06 0.15 0.3 Total 0.3 0.2 0.5 1

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