5.4
Question 12, 5.4.31
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Suppose there is a $12.9 \%$ probability that a randomly selected person aged 30 years or older is a jogger. In addition, there is a $26.8 \%$ probability that a randomly selected person aged 30 years or older is female, given that he or she jogs. What is the probability that a randomly selected person aged 30 years or older is female and jogs? Would it be unusual to randomly select a person aged 30 years or older who is female and jogs?

The probability that a randomly selected person aged 30 years or older is female and jogs is $\square$ (Round to three decimal places as needed.).

Step 1 ：Given that the probability of a person aged 30 years or older being a jogger, denoted as P(B), is 12.9% or 0.129.

Step 2 ：Also given that the probability of a person aged 30 years or older being female given that he or she jogs, denoted as P(A|B), is 26.8% or 0.268.

Step 3 ：We are asked to find the probability that a randomly selected person aged 30 years or older is female and jogs, denoted as P(A and B).

Step 4 ：We can use the formula for conditional probability to find this, which is P(A and B) = P(A|B) * P(B).

Step 5 ：Substituting the given values into the formula, we get P(A and B) = 0.268 * 0.129 = 0.034572000000000006.

Step 6 ：Rounding this to three decimal places, we get P(A and B) = 0.035.

Step 7 ：So, the probability that a randomly selected person aged 30 years or older is female and jogs is \(\boxed{0.035}\).