Question

a home pregnancy test was given to women, then pregnancy was verified through blood tests. the following table shows the home pregnancy test results.

	pregnant	not pregnant	total
negative	4	69	73
total	84	76	160

find the following. round answers to 4 decimal places.
a. p(positive | pregnant) = 0.9524
b. what is the probability that the woman is pregnant given that the test is positive?
c. given that a woman is pregnant, what is the probability that the test is negative?
d. p(not pregnant | negative) = 0.0548

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of the table values, if $A$ and $B$ are events, $P(A|B)$ is the number of elements in $A\cap B$ divided by the number of elements in $B$.

Step2: Solve part b

We want to find $P(\text{Pregnant}|\text{Positive})$. The number of pregnant - and - positive women is $80$, and the number of positive - result women is $87$. So $P(\text{Pregnant}|\text{Positive})=\frac{80}{87}\approx0.9195$.

Step3: Solve part c

We want to find $P(\text{Negative}|\text{Pregnant})$. The number of pregnant - and - negative women is $4$, and the number of pregnant women is $84$. So $P(\text{Negative}|\text{Pregnant})=\frac{4}{84}\approx0.0476$.

Answer:

b. $0.9195$
c. $0.0476$