Statistics  Probability
posted by Esther .
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 underperform 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 underperforming fund in it?

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