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) =

(d) What statement is true about the probability of getting a false positive?

The probability of a false positive increases after a positive test result is obtained.

The probability of a false positive decreases after a positive test result is obtained.     

The probability of a false positive is not affected by the result of the test.

*Significant Digits: Here are some probabilities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero digit.

0.123      0.0123      0.0120      0.00123     0.102      0.350      0.300

Was she actually pregnant? Yes           No Positive Test Result      480           15 Negative Test Result      6              499

Explanation / Answer

Ans:

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

=0.48/0.486=0.988

b)P(false positive)=P(positive/not pregnent)=P(positive and not pregnent)/P(not pregnent)=0.015/0.514=0.029

c)P(not pregnent/positive)=P(positive and not pregnent)/P(positive)=0.015/0.495=0.030

d)The probability of a false positive is not affected by the result of the test.

Pregnant Yes No Total Positive 480 15 495 Negative 6 499 505 Total 486 514 1000 Joint Prob. Distribution Yes No Total Positive 0.48 0.015 0.495 Negative 0.006 0.499 0.505 Total 0.486 0.514 1

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