Question

A researcher investigating the accuracy of a certain pregnancy test finds the following

TEST RESULT
TRUE STATUS	(+)	(-)	TOTAL
PREGNANT	48	2	50
NOT PREGNANT	38	912	950
TOTAL	86	914	1000

a) What is the probability that a randomly selected woman taking this pregnancy test is pregnant?

b) What is the probability that a randomly selected woman taking this pregnancy received a false positive (a false positive is testing positive and not being pregnant)?

c) Given a woman receives a positive pregnancy test, what is the probability that she is truly pregnant?

d) Are Test Result and True Status independent? Support your conclusion using probability formulas.

Answer 1

(a)

From the given data, the following Table is calculated:

	Test Positive	Test Negative	Total
Pregnant	48 TRUE POSITIVE	2 FALSE NEGATIVE	50
Not pregnant	38 FALSE POSITIVE	912 TRUE NEGATIVE	950
Total	86	914	1000

P(Pregnant) = 50/1000 = 0.05

So,

Answer is:

0.05

(b)

P( false positive ) = 38/1000 = 0.038

So,

Answer is:

0.038

(c)
P(Pregnant/ Test Positive) = P(Pregnant AND Test Positive) / P(Test Positive)

                                       = 48/86 = 0.5581

So,

Answer is:

0.5581

(d)

P(Pregnant) = 50/1000 = 0.05

P(Test Positive) = 86/1000 = 0.086

So,

P(Pregnant) X P(Test Positive) =0.05 X 0.086 = 0.0043

But,

P(Pregnant AND Test Positive) = 48/1000 = 0.048

Since P(Pregnant) X P(Test Positive)   = 0.0043 P(Pregnant AND Test Positive) = 0.048, we Conclude:

Test Result and True Status are not independent.