Question

Males and females are observed to react differently to a given set of circumstances. It has been observed that 70% of females react positively to these circumstances where as 40% of males react positively. A group of 20 people, 15 females and 5 males, was subjected to these circumstances, and they were asked to describe their reactions on a written questionnaire. A response picked at random was negative. What is the probability that it was of that of a male?

M = Male

F = Female

P(Male) = ?

P(Female) = ?

P(Reacted Negatively | M) = ?  

P(Reacted Negatively | F) = ?

P(Reacted Negatively) = ?

P(Male | Reacted Negatively) = ?

Answer 1

Based on the information:

Reaction	Female	Male
Positive	70%	40%
Negative	30%	60%

n = 20

Female = 15 & Male = 5

P(F) = 15/20 = 0.75

P(M) = 5/20 = 0.15

Reaction	Female	Male	total
Positive	10.50	2.00	12.50
Negative	4.50	3.00	7.50
Total	15.00	5.00	20.00

1. P(male) = P(Male and reacted negative) = 3/ 20 = 0.15

2. P (female) = P(Female and reacted negative) = 4.5 / 20 = 0.225

3. P(Reacted Negatively | M) = P(reacted negative and male)/ P(male) = 0.15/ 0.25 = 0.60

4. P(Reacted Negatively | F) = P(reacted negative and male)/ P(male) = 0.225/ 0.75 = 0.30

5. P(Reacted Negatively) = 7.5 /20 = 0.375

6. P(Male | Reacted Negatively) = P(reacted negative and male)/ P(male) = 0.15 / 0.375 = 0.40