Pregnancy Test: A pregnancy testing device is used by 1000 different women from

Question

Pregnancy Test: 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) =

(d) What statement is true about the probability of getting a false positive?The probability of a false positive decreases after a positive test result is obtained.The probability of a false positive increases after a positive test result is obtained.     The probability of a false positive is not affected by the result of the test.

Was she actually pregnant? Yes           No Positive Test Result      482           12 Negative Test Result      5              501

Explanation / Answer

a) P(result is correct) = (482+501)/(482+12+5+501) =0.983

b) P(false positive)=12/(482+12+5+501) =0.012

c) P(not pregnant | positive test result) = P(not pregnant and positive test result)/P(positive test result)= 12/(482+12) =0.024

d) The probability of a false positive decreases after a positive test result is obtained because the denominator increases but the numerator remains the same i.e 12 (numerator)

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