Question

The probability that Andrew has heart disease is 0.9. Andrew takes a test for the disease that has an accuracy rate of 75%. What is the probability that Andrew has heart disease and the test accurately predicts it?

Answer 1

Let A be the event 'Andrew has heart disease'. Then P(A) = 0.9.
Let B be the event 'test gives correct result'. Then P(B) = 0.75.
The probability of A and B occurring is given by:
\[\large P(A\cap B)=P(A)\times P(B)\]