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 FemaleType A 65 85Type B 38 12Compare 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)
Accepted Solution
A:
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)