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.

Was she actually pregnant?
-----------------------------Yes No
Positive Test Result 482 13
Negative Test Result 5 500

A) Using the relative frequency approximation of probabilities, what is the probability that the device is correct? Enter your answer in decimal form rounded to the 3rd decimal place.

B) Suppose you are a woman about to take the test. Prior to taking the test, what is the probability of a false-positive? Enter your answer in decimal form rounded to the 3rd decimal place.

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? Enter your answer in decimal form rounded to the 3rd decimal place.

I can't figure out where I went wrong in my calculation for all those questions. I had the wrong answers for all of them. Could someone please explain how you would get your answer. Thank you!!!

Explanation / Answer

Ans:

a)P(device is correct) = P(pregnant and positive result) + P(not pregnant and negative result)

=(482/1000)+(500/1000)

=0.982

b)P(false positive) =13/1000=0.013

c)It will be wrong when women in not pregnant actually.

So,we have to find P(not pregnant/positive)

P(positive)=495/1000=0.495

P(not pregnant/positive)=P(not pregnant and positive)/P(positive)=(13/1000)/(495/1000)

=13/495

=0.026

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