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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?

Answer :

This problem of probability can be solved using Baye's Theorem . In simple terms , Bayes' Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event. Hence , proceeding accordingly -

Given in the question is :

P(Males reacting negatively = M) = 1-40%= 60% = 60/100

P(Females reacting negatively = F) = 1-70%= 30% = 30/100

Now , P(Females' response being selected= f) = 15/20
P(Males' response being selected = m ) = 5/20

P(M/m) = P(M) P(m)/ P(M) P(m) + P(F) P(f)
⇒ 5/30 × 60/100 ÷ 5/30 × 60/100 + 15/20 × 30/100

⇒ 300/300+450
⇒ 300/750

⇒ 2/5

To know more about probability , go to https://brainly.com/question/11234923

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