5. Professor Frank Nabarro insists that all senior physics majors take his notorious physics aptitude test....

5. 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 55% 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.]

Solutions

Expert Solution

given :

P(fail | not going on to a career in physics) = 100% = 1

P(fail | going on to a career in physics) = 55% = 0.55

P(going on to a career in physics) = 0.70

P(not going on to a career in physics) = 1-0.70 = 0.30

P(fail) = P(fail | not going on to a career in physics)*P(not going on to a career in physics) + P(fail | going on to a career in physics)*P(going on to a career in physics)

= 1*0.30 + 0.55*0.70

P(fail) = 0.685

bayes theorem :

Assuming that you fail the test, what is the probability that you will not go on to a career in physics :

using bayes theorem :

P(not go on to a career in physics | fail) = P(fail | not going on to a career in physics)*P(not going on to a career in physics) / P(fail)

= 1*0.30 / 0.685

P(not go on to a career in physics | fail) = 0.438

Assuming that you fail the test, the probability that you will not go on to a career in physics is 0.438

P.S. (please upvote if you find the answer satisfactory)

orchestra answered 1 year ago

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