A pregnancy testing device is used by 1000 different women from a population of

Question

A pregnancy testing device is used by 1000 different women from a population of women who think they might be pregnant. The results are depicted in the contingency table below. Here, a positive test result means pregnancy is detected.

(a) Using the relative frequency approximation of probabilities, what is the probability that the device is correct? Round your answer to 3 significant digits.*
P(result is correct) =

(b) Suppose you are a woman about to take the test. Prior to taking the test, what is the probability of a false-positive? Round your answer to 3 significant digits.*
P(false positive)

(c) Suppose you are a woman who takes the test and it comes back positive. Now, what is the probability that the test result is wrong? Round your answer to 3 significant digits.*
P(not pregnant | positive test result) =

Was she actually pregnant? Yes           No Positive Test Result      479           13 Negative Test Result      5              503

Explanation / Answer

Ans:

a)P(result is correct)=P(positive/actually pregnent)=P(positive and actually pregnent)/P(actually pregnent)

=0.479/0.484=0.990

b)P(false positive)=P(positive/not pregnent)=P(positive and not pregnent)/P(not pregnent)=0.013/0.516=0.025

c)P(not pregnent/positive)=P(positive and not pregnent)/P(positive)=0.013/0.492=0.026

Pregnant Yes No Total Positive 479 13 492 Negative 5 503 508 Total 484 516 1000 Joint Prob. Distribution Yes No Total Positive 0.479 0.013 0.492 Negative 0.005 0.503 0.508 Total 0.484 0.516 1

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