Question

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?

Answer 1

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:


`P(G|F)= (0.3)/(0.6) =0.5`

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

Answer 2

30% probability that an undergraduate is in a greek organization given that the undergraduate is a female

Explanation:

The conditional probability formula is used to solve this question:

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this problem, we have that:

60% of undergraduates are female.

100 - 60 = 40% are male.

30% belong to the organization.

Of those, 40% are male.

So 0.3*0.4 = 0.12 are male and belong to the organization.

0.3 - 0.12 = 0.18 are female and belong to the organization.

What is the probability that an undergraduate is in a greek organization given that the undergraduate is a female?

Event A: Being female, so P(A) = 0.6.

Event B: Being in the organization.

`P(A \cap B) = 0.18`

So

`P(B|A) = (P(A \cap B))/(P(A)) = \fra{0.18}{0.6} = 0.3`

30% probability that an undergraduate is in a greek organization given that the undergraduate is a female