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 50% of the seniors who do go on to a career in physics still fail the test. Further, 90% 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

we can use Bayes theorem

for two events A and B

let the event where one fails be F and where one does not pursue career in physics be N

probability that a person will pursue career in physics

P (N') = 90 / 100 = 0.9

so,

probability that a person will not pursue career in physics

P(N) = 1 - 0.9

P(N) = 0.1

if a person fails because he/she don't like physics

then

P (F/N) = 1

if person pursue career in physics but still fail

P (F /N') = 50 / 100 = 0.5

Therefore,probability that you will not go on to a career in physics

P (N/F) = (1) (0.1) / [(1) (0.1) + (0.5)(0.9)]

P (N/F) = 0.1818