Question

it is estimated that 26% of all california adults are college graduates and that 31% of california adults exercise regularly. it is also estimated that 21% of california adults are both college graduates and regular exercisers. answer the questions below. (if necessary, consult a list of formulas.) (a) among california adults, what is the probability that a randomly - chosen regular exerciser is a college graduate? round your answer to 2 decimal places. (b) what is the probability that a california adult is a regular exerciser, given that he or she is a college graduate? round your answer to 2 decimal places.

Explanation:

Step1: Define the events

Let $A$ be the event that a California adult is a college - graduate, $P(A)=0.26$. Let $B$ be the event that a California adult is a regular exerciser, $P(B)=0.31$, and $P(A\cap B)=0.21$.

Step2: Use the formula for conditional probability for part (a)

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Substitute the known values: $P(A|B)=\frac{0.21}{0.31}\approx0.68$.

Step3: Use the formula for conditional probability for part (b)

The formula for conditional probability is $P(B|A)=\frac{P(A\cap B)}{P(A)}$. Substitute the known values: $P(B|A)=\frac{0.21}{0.26}\approx0.81$.

Answer:

(a) $0.68$
(b) $0.81$