In a major midwestern university, 60% of all undergraduates are female, 30% belong to a greek organization (fraternity or sorority) and 40% of all males belong to a greek organization. what is the probability that an undergraduate is in a greek organization given that the undergraduate is a female?

Percentage of undergraduate that are female = P(F) = 60%= 0.6
Percentage of females who belong to Greek organization = P(F ∩ G) = 30% = 0.03

We are to find probability that an undergraduate is in a Greek organization given that the undergraduate is a female. In mathematical form we can write that we are to find P(G|F)

P(G|F) = P(F ∩ G) / P(F) 

Using the values, we get:

[tex]P(G|F)= \frac{0.3}{0.6} =0.5[/tex]

Therefore, the probability that an undergraduate is in a Greek organization given that the undergraduate is a female is 0.5