Problem 129E

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

Solution

Step 1 of 2

We have to find the probability of getting negative reaction that it is from male

Let M be the reaction from the male

Let F be the reaction from the female

Let N be the negative reaction

Given that

Probability of female reacts positively is 0.7

Probability of female reacts negatively is P(N/F)=1-0.7

=0.3

Probability of male reacts positively is 0.4

Probability of male reacts negatively is P(N/M)=1-0.4

=0.6

The no.of survey people is 20 in that 15 female and 5 male

Probability of female is P(F)=15/20

=0.75

Probability of male is P(M)=5/20

=0.25