6. Home pregnancy tests, like all medical tests, are not perfectly accurate. Sup

Question

6. Home pregnancy tests, like all medical tests, are not perfectly accurate. Suppose one such test has an accuracy level such that if a woman is pregnant there is a 12% chance that the test will fail to show it. On the other hand, if the woman is not pregnant there is still a 3% chance that the test will incorrectly say that she is. a) If a woman is pregnant what is the chance that the test will detect it? b) Based on other factors, Joan estimates there is an 80% chance that she is pregnant Therefore, Joan takes a pregnancy test. What is the probability that the test will indicate that she is pregnant? c) Joan looks at the test result and it does indicate that she is pregnant. Given this test result, what is the probability that she is pregnant? d) Pamela has also taken this particular home pregnancy test. Before taking the test, she estimated there was a 75% chance that she's pregnancy. She takes the test but it indicates that she is not pregnant. What is the probability Pamela actually is pregnant?

Explanation / Answer

a) P(detecting pregnancy) = 1 - 0.12 = 0.88

b) P9test will indicate that she is pregnant)

= P(pregnant and positive) + P(not preganant and positive)

= 0.8x0.88 + 0.2x0.03

= 0.71

c) P(she is pregant | test indicates preganancy)) = P(pregnant and positive)/ P(positive)

= 0.8x0.88 / 0.71

= 0.99155

d) P(pregnant | test indicates not pregnant)

= P(pregnant and negative)/ P(negative)

= 0.75x0.12/(0.75x0.12 + 0.25x0.97)

= 0.2707

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.