Question

Professor Frank Nabarro insists that all senior physics majors take his notorious physics aptitude test. The test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 60% of the seniors who do go on to a career in physics still fail the test. Further, 70% of all senior physics majors in fact go on to a career in physics. Assuming that you fail the test, what is the probability that you will not go on to a career in physics? (Round your answer to four decimal places.) HINT [See Example 3.]

Answer 1

Let A denote the event that the physics major go on to a career in physics

And B denote the event that the physics major will fail the test

P(A) = 0.7

Thus, P(A') = 1 - P(A) = 0.3

P(B|A) = 0.6

Also, P(B|A') = 1

Probability that a random selected physics major fail the test,

P(B) = P(B|A)*P(A) + P(B|A')*P(A')

= 0.6*0.7 + 1*0.3 = 0.72

Probability that you will not go on to a career in physics, assuming you fail the test

= P(A'|B)

= P(B|A')*P(A')/P(B)

= (1 * 0.3)/0.72 = 0.4167