ANSWERS:
A. 0.28 ( 28.41% )
B. 89.29%
EXPLANATIONS:
(a) The probability of a randomly chosen U.S. adult investing in both stocks and fixed income instruments is given as 0.25. The probability of a U.S. adult investing in fixed income instruments is 0.88. Using the formula for conditional probability, we have:
P(invests in stocks | invests in fixed income instruments) = P(invests in both stocks and fixed income instruments) / P(invests in fixed income instruments)
= 0.25 / 0.88
= 0.2841 (rounded to the nearest hundredth)
Therefore, the probability that a randomly chosen U.S. adult invests in stocks, given that he or she invests in fixed income instruments is 0.28 (rounded to the nearest hundredth).
To convert A to a percentage, simply multiply it by 100:
A = 0.2841
A as a percentage = 0.2841 x 100% = 28.41% (rounded to two decimal places)
(b) The probability of a randomly chosen U.S. adult investing in both stocks and fixed income instruments is 0.25, and the probability of a U.S. adult investing in stocks is 0.28. Using the formula for joint probability, we have:
P(invests in both stocks and fixed income instruments) = P(invests in stocks) × P(invests in fixed income instruments)
= 0.28 × 0.88
= 0.2464
The probability that a randomly chosen stock investor also invests in fixed income instruments is 0.25 / 0.28 = 0.8929 (rounded to the nearest hundredth), which is equivalent to 89.29%.