Question

The probability that Emma has heart disease is 0.6. She decides to take a test for the disease that is 80% accurate. What is the probability that Emma has heart disease and the test predicts heart disease?

Answer 1

0.6 x 0.8 = 12/25 The probability that Emma has heart disease and the test predicts it is 48%

Answer 2

The probability that Emma has heart disease and the test predicts heart disease is:

48%

Explanation:

Let A denote the event that Emma has a heart disease.

and B denote the event that the test predicts accurate.

Hence, A∩B denote the event that Emma has heart disease and the test predicts heart disease.

From the given equation we have:

P(A)=0.6

and P(B)=80%=0.8

As we know that event A and event B are independent.

Hence, we have:

P(A∩B)=P(A)×P(B)

⇒ P(A∩B)=0.6×0.8

⇒ P(A∩B)=0.48=48%

Hence, the probability is:

48%