ifty-six percent of all American workers have a workplace retirement plan, 69% h
ID: 3331731 • Letter: I
Question
ifty-six percent of all American workers have a workplace retirement plan, 69% have health insurance, and 84% have health insurance given that they have a retirement plan, we select a worker at random. a) What is the probability he has health insurance and a retirement plan? PCH)-Heedth Tsnance- 0.6 PCRIH)- o-94 0.34x0.56 0.4704 What is the probability that he has a retirement plan given that he has health PCRIH)- PCHond R)/PCH) 204704 b·64 0.6317 b) insuraPRH)-PCHort Ry/PH) c) What is the probability he has health insurance or a retirement plan? 07746 d) What is the probability that he does not have either health insurance or a retirement plan? Are having health insurance and a retirement plan independent events? Demonstrate why or why not. e)Explanation / Answer
let health insuarance is H and workplace retirement plan is R
a)hence P(R n H)=P(R)*P(H|R) =0.56*0.84=0.4704
b)P(R|H)=P(R n H)/P(H)= 0.4704/0.69= 0.6817
c) P(H U R) =P(H)+P(R)-P(H nR) =0.69+0.56-0.4704=0.7796
d)P( HuR)c =1-P(HUR) =1-0.7796 =0.2204
e)as P(H)*P(R)=0.69*0.56 =0.3864 which is not equal to P(H n R) . therefore not independent.
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