A survey was conducted in a community Sixty percent of the r

A survey was conducted in a community. Sixty percent of the respondents were female. Thirty percent of the female respondents indicated that they had utilized the community library within the previous seven days. 22% of the male respondents indicated using the community library during the same period.

1. If a person is chosen at random from all the respondents, what is the probability that is a male who did not use the library within the previous seven days?

2.  If a person is chosen at random from all the respondents, what it the probability that they did use the library within the previous seven days?

3.  If a person is chosen at random and its learned that they had used the library within the last seven days, what is the probability that it was a female?

Solution

1. probability that is a male who did not use the library within the previous seven days= 0.40*0.78=0.312

2. probability that they did use the library within the previous seven days= 0.40*0.22+0.60*0.30= 0.268

3. = P(female, used library)/P(person, used library) = 0.60*0.30/(0.40*0.22+0.60*0.30) = 0.6716