Suppose that 10% of the undergraduates at a certain university are foreign students, and that 25% of the graduate students are foreign. If there are four times as many undergraduates as graduate students, given that a randomly selected student is foreign, what is the probability that the student is an undergraduate

0.6154 = 61.54% probability that the student is an undergraduate

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

In which

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

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Foreign

Event B: Undergraduate.

There are four times as many undergraduates as graduate students

So 4/5 = 80% are undergraduate students and 1/5 = 20% are graduate students.

Probability the student is foreign:

10% of 80%

25% of 20%. So

Probability that a student is foreign and undergraduate:

10% of 80%. So

What is the probability that the student is an undergraduate?

0.6154 = 61.54% probability that the student is an undergraduate