A mutual fund company has six funds that invest in the U.S. market and four funds that invest in foreign markets. An investor wishes to create a mutual fund portfolio composed of two U.S. funds and two foreign funds. Unknown to this investor, one of the U.S. funds and one of the foreign funds will seriously under-perform next year.

Question

A mutual fund company has six funds that invest in the U.S. market and four funds that invest in foreign markets.  An investor wishes to create a mutual fund portfolio composed of two U.S. funds and two foreign funds.  Unknown to this investor, one of the U.S. funds and one of the foreign funds will seriously under-perform next year.

If the investor selects funds for his portfolio at random, what is the probability that he will have selected a portfolio with at least one under-performing fund in it?

MathMate · Accepted Answer

Probability of choosing ONLY good funds from the US market
= (5/6)*(4/5) = 2/3
Probability of choosing ONLY good funds from the foreign market
= (3/4)*(2/3)=2/4=1/2

Probability of choosing ONLY good funds from both markets = (2/3)*(1/2)=1/3

Probability of choosing at least one bad fund
= 1- (1/3) = 2/3