what is the probability

Question

It is estimated 30% of all adults in United States invest in stocks and that 85% of U.S. adults have investments in fixed income instruments (savings accounts, bonds, etc.). It is also estimated that 25% of U.S. adults have investments in both stocks and fixed income instruments. (a)What is the probability that a randomly chosen stock investor also invests in fixed income instruments? Round your answer to the nearest hundredth. (b)What is the probability that a randomly chosen U.S. adult invests in stocks, given that he or she invests in fixed income instruments? Round your answer to the nearest hundredth.

Answer 1

These are questions of conditional probability.

In symbols: P(A|B)=P(A&B)/P(B)

P(S)=.3

P(F)=.85

P(F&S)=.25

P(F|S)=.25/.3=.83

P(S|F)=.25/.85=.29