Answer: Our required probability is 0.0690.
Explanation:
Since we have given that
Probability that seniors who do go on to a career in physics still fail the test P(F|P) = 60%
Probability that seniors who do not go to a career in physics fail the test = 1-0.6=0.4=40%
Probability that senior physics majors in fact go on to a career in physics = P(P) = 90%
Probability that he will not go on to a career in physics given that he fail the test is given by

Hence, our required probability is 0.0690.