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

Answer 1

Answer:

P(Male or Type B) > P(Male | Type B)

Step-by-step explanation:

Total Female = 85 type A, 12 type B  ⇒ 97 Female.

Total Male = 65 type A, 38 type B   ⇒ 103 Male

Total type A = 65 + 85 = 150

Total type B = 12 + 38 = 50

total number of people = 97 + 103 = 200

Then the probability would be:

P(Male | Type B) = $\frac{number of male in B}{total number of male}$

                           = $\frac{38}{103}$

                           = 0.368

P(Male or Type B) = $\frac{total number of male + (total number of people in B - total number of male in B)}{total number of male}$

                              =  $\frac{103 + (50 - 38)}{200}$

                              = $\frac{103 + 12}{200}$

                              = $\frac{115}{200}$

                              = 0.575

 Hence, P(Male or Type B) > P(Male | Type B)