100 women use a new pregnancy test 44 of the women are actua

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. Calculate the probability for each event.

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)

Solution

Total number of wome who undergone test: 100.

Women who are pregnant: 44.

Women who are not pregnant: 56.

Pregnant women(44) who test positive: 35.

Success ratio for the test on pregnant women: 35 / 44 = 0.8.

Failure ratio for the test on pregnant women: 1 - 0.8 = 0.2 (9 women).

Non-pregnant women(56) who test positive: 8.

Failure ratio for the test on non-pregnant women: 8 / 56 = .14.

Success ratio for the test on non-pregnant women: 1 - .14 = .86 (48 women).

Total success ratio: Women who got correct results: 35 + 48 = 83. (0.83 is the overall success rate of the test)

Total failure ratio: Women who got incorrect results: 9 + 8 = 17. (0.17 is the overall failure rate of the test)

Coming to your questions:

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

Not pregnant women: 56.(total cases)

Of them, who got negative test results: 48. (favorable cases).

So, probability: 48 / 56 = 0.86

2.A randomly selected test is positive

Total women: 100 (total cases)

Positively tested women: 35 + 8 = 43. (favorable cases)

So, probability: 43 / 100 = 0.43

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

Women who are tested negative: 9 + 48 = 57. (total cases)

Women who are pregnant of these people = 9. (favorable cases)

So, probability: 9 / 57 = 0.16

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

Total women: 100. (total cases)

Incorrect results women: 9 + 8 = 17. (favorable cases)

So, probability: 17 / 100 = .17.