The following table gives the sex and age group of college students at a Midwestern university. A student is to be selected at random. Given that the selected student is female, the conditional probability that she is 25 to 34 years old is:

Question

The following table gives the sex and age group of college students at a Midwestern university.  A student is to be selected at random. Given that the selected student is female, the conditional probability that she is 25 to 34 years old is:

Quizplus · Accepted Answer

To find the conditional probability, we use the formula: P(A|B) = P(A and B) / P(B).
We are given that the selected student is female, so P(B) = proportion of females = (157+102+90)/(157+102+90+44+33) = 0.6.
We are also given that the selected student is 25 to 34 years old and female, so P(A and B) = proportion of females who are 25 to 34 years old = 90 / (157+102+90) = 0.3636.
Therefore, P(25 to 34 years old|female) = P(A|B) = P(A and B) / P(B) = 0.3636 / 0.6 = 0.204.

The Following Table Gives the Sex and Age Group of College