One of the major talking points about the ACA—also known as “Obamacare”—is about

Question

One of the major talking points about the ACA—also known as “Obamacare”—is about preexisting conditions. Let E be the event that an American has a preexisting condition, and suppose2 that 6% of Americans have a preexisting condition(s). Let A be the event that a person’s insurance cost will rise after the ACA goes into effect. Suppose that the probability that a person’s insurance cost will rise given that the person has a preexisting condition is 32%, while the probability that a person’s insurance cost will rise given that the person does not have a preexisting condition is 54%. Compute the probability that a person has a preexisting condition given that his or her insurance cost has risen. Get a final answer in between zero and one.

Explanation / Answer

Ans:

Given that

P(prexisting condition)=0.06

P(insurance cost rise/prexisting condition)=0.32

P(insurance cost rise/NOT prexisting condition)=0.54

P(insurance cost risen)=0.32*0.06+0.54*(1-0.06)=0.0192+0.5076=0.5268

P(preexisting condition/insurance cost risen)=P(insurance cost risen/prexisting condition)*P(preexisting condition)/P(insurance cost risen)

=0.32*0.06/0.5268

=0.0192/0.5268

=0.0364

P(preexisting condition/insurance cost risen)=0.0364

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