Question

A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table below:

Male Female
Type A 65 85
Type B 38 12


Compare P(Female | Type B) with P(Female or Type B). (5 points)

P(Female | Type B) < P(Female or Type B)
P(Female | Type B) = P(Female or Type B)
There is not enough information.
P(Female | Type B) > P(Female or Type B)

Answer 1

P(Female | Type B) < P(Female or Type B)

Explanation:

just took the test

Answer 2

Answer: P(Female | Type B) < P(Female or Type B)

In this question, there is 85 Type A female and 12 type B female which makes a total of 97 female. There is also 38 male Type B from a total of 113 male. Then the probability would be:
female type B = type B female/ total female
female type B = 12/97


Female or Type B= Female + type B male/ total
Female or Type B= 97+38/ 97+113= 135/ 210

It should be clear that P(Female | Type B) < P(Female or Type B)