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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, 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.) HINT [See Example 3.]

Respuesta :

Answer: Our required probability is 0.0690.

Step-by-step 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

[tex]\dfrac{P(F|P')\times P(P')}{P(F)}\\=\dfrac{0.4\times 0.10}{0.4\times 0.1+0.6\times 0.9}\\\\=\dfrac{0.04}{0.04+0.54}\\\\=\dfrac{0.04}{0.58}\\\\=0.06896\\\\\approx 0.0690[/tex]

Hence, our required probability is 0.0690.

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