100 women use a new pregnancy test, 44 of the women are actually pregnant. Of th

Question

100 women use a new pregnancy test, 44 of the women are actually pregnant. Of the women who are pregnant, 35 test positive. Of the women who are not pregnant, 8 of them test positive. Draw tree diagram and Calculate the probability for each event. Please write neatly and explain. Thank you so much!

1. A randomly selected test is negative, given the woman is not pregnant

2. A randomly selected test is positive

3. A randomly selected test is from a woman who is pregnant given it is negative

4. A randomly selected test is incorrect (false-positive or false-negative)

Explanation / Answer

P(Pr) = 44/100 = 0.44 and P(Pr') = 0.56

P(+ve|Pr) = 34/44 = 0.7955

P(+ve|Pr') = 8/56 = 0.1429

P(-ve|Pr) = 9/44 = 0.2046

P(-ve|Pr') = 48/56 = 0.8571

(1) Probability that a randomly selected test is negative, given the woman is not pregnant

P(-ve|Pr') = 48/56 = 0.8571

(2)

Probability that randomly selected test is positive

P(+ve) = P(+ve|Pr) + P(+ve|Pr') = 0.7955 + 0.1429 = 0.9384

(3)

Probability that a randomly selected test is from a woman who is pregnant given it is negative

P(Pr|-ve) = P(-ve|Pr)*P(Pr) / (P(-ve|Pr)*P(Pr) + P(-ve|Pr')*P(Pr')) = 0.2046*0.44 / (0.2046*0.44 + 0.8571*0.56) = 0.1579

(4)

Probability that a randomly selected test is incorrect

P(+ve|Pr') = 8/56 = 0.1429

P(-ve|Pr) = 9/44 = 0.2046

Required probability = 0.1429 + 0.2046 = 0.3475

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