Total number of people: 65 + 85 +38 +12 = 200
Total male = 65 +38 = 103
Total women: = 200-103 = 97
Total Type A = 65+85 = 150
Total Type B = 38+12 = 50
P(male or type b ) = 103/200 + 50/200 - 38/200 = 0.515 + 0.25 - 0.19 = 0.765 - 0.19 = 0.575
P(male | type b ) = 38/50 = 0.76
The answer is P(male or type b ) < P(male | type b )
