A small town has 5000 adult males and 7000 adult females. A sociologist conducted a survey and found that 40% of the males and 30% of the females drink heavily. An adult is selected at random from the town. What is the probability, rounded to four decimal places, that the person is male M or drinks heavily DH?

Question

A small town has 5000 adult males and 7000 adult females. A sociologist conducted a survey and found that 40% of the males and 30% of the females drink heavily. An adult is selected at random from the town. What is the probability, rounded to four decimal places, that the person is male M or drinks heavily DH? ​

Quizplus · Accepted Answer

The probability that the person is male is 5000/(5000+7000) = 5/12. 
The probability that the person drinks heavily is (0.4)*5000/12000 + (0.3)*7000/12000 = 0.35. 
The probability that the person is male or drinks heavily is Pr(M∪DH) = Pr(M) + Pr(DH) - Pr(M∩DH) 
Pr(M∩DH) = Pr(DH| M) * Pr(M) = (0.4)*5000/12000 = 1/6 
Therefore, Pr(M∪DH) = 5/12 + 0.35 - 1/6 = 0.5917 rounded to four decimal places. So, the best choice is C.

A Small Town Has 5000 Adult Males and 7000 Adult