Question

it is estimated that 30% of all adults in the united states invest in stocks and that 87% of u.s. adults have investments in fixed - income instruments (savings accounts, bonds, etc.). it is also estimated that 24% of u.s. adults have investments in both stocks and fixed - income instruments. answer the questions below. (if necessary, consult a list of formulas.) (a) what is the probability that a randomly chosen stock investor also invests in fixed - income instruments? round your answer to 2 decimal places. (b) what is the probability that a randomly chosen u.s. adult invests in stocks, given that s/he invests in fixed - income instruments? round your answer to 2 decimal places.

Explanation:

Step1: Define the events

Let $A$ be the event that an adult invests in stocks, $P(A)=0.3$. Let $B$ be the event that an adult invests in fixed - income instruments, $P(B) = 0.87$, and $P(A\cap B)=0.24$.

Step2: Calculate the probability for part (a)

We want to find $P(B|A)$. By the formula for conditional probability $P(B|A)=\frac{P(A\cap B)}{P(A)}$. Substitute the known values: $P(B|A)=\frac{0.24}{0.3}=0.80$.

Step3: Calculate the probability for part (b)

We want to find $P(A|B)$. By the formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Substitute the known values: $P(A|B)=\frac{0.24}{0.87}\approx0.28$.

Answer:

(a) 0.80
(b) 0.28