When a pregnancy testA was performed on 500 pregnant women, 3 came out with nega

Question

When a pregnancy testA was performed on 500 pregnant women, 3 came out with negative results. When pregnancy test B was performed on 300 pregnant women, 2 came out to be negative.

a. If a randomly chosen pregnant woman had a negative test result, what is the probability that she was subjected to test A?

b. If possible find

the sensitivity of test A

the specificity of testA.

c. Mary who is pregnant did test A and Jane, who is also pregnant did test B. What is the probability that they both got positive results?

Explanation / Answer

probability of negative test result =P(test A and negative result+test B and negative test result)

=(500/800)*(3/500)+(300/800)*(2/300) =5/800

therefore probability that she was subjected to test A,given tested negative

=P(test A and negative result)/P( tested negative) = =(500/800)*(3/500)/(5/800) =3/5

b)

sensitivity of test A =P(tested positive among pregnant women) =(500-3)/500 =497/500=0.994

we can not calculate specificity of testA as specificity =P(tested negaitve among non -pregnant women) for which we do not have sufficient data.

c)probability that they both got positive results =P( Mary got positive result)*P(Jane got positive result)

=(497/500)*(298/300) =0.987373

please revert for any clarificaiton required

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