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 45% 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.)

Answer 1

Given,

P(Go for physics) = 0.70

So P(Not go for physics) = 1 - 0.70 = 0.30

P(Fail | Go for physics) = 0.45

P(Fail | Not go for physics) = 1

Hence by Bayes' theorem:

P(Not go for physics | Fail)

0.30 +1 0.30 +140.70 * 0.45

= 0.4878