Suppose there is a $11.9 \%$ probability that a randomly selected person aged 25 years or older is a jogger. In addition, there is a $20.6 \%$ probability that a randomly selected person aged 25 years or older is male, given that he or she jogs. What is the probability that a randomly selected person aged 25 years or older is male and jogs? Would it be unusual to randomly select a person aged 25 years or older who is male and jogs?
The probability that a randomly selected person aged 25 years or older is male and jogs is (Round to three decimal places as needed.).
Answer
Final Answer: The probability that a randomly selected person aged 25 years or older is male and jogs is \(\boxed{0.025}\).
Step 1 ：We are given two probabilities:
Step 2 ：1. The probability that a randomly selected person aged 25 years or older is a jogger, denoted as \(P(J) = 11.9\% = 0.119\).
Step 3 ：2. The probability that a randomly selected person aged 25 years or older is male, given that he or she jogs, denoted as \(P(M|J) = 20.6\% = 0.206\).
Step 4 ：We are asked to find the probability that a randomly selected person aged 25 years or older is male and jogs, denoted as \(P(M \cap J)\).
Step 5 ：From the definition of conditional probability, we know that \(P(M \cap J) = P(M|J) \times P(J)\).
Step 6 ：So, we can calculate \(P(M \cap J)\) by multiplying \(P(M|J)\) and \(P(J)\).
Step 7 ：\(P(M \cap J) = P(M|J) \times P(J) = 0.206 \times 0.119 = 0.024514\)
Step 8 ：Final Answer: The probability that a randomly selected person aged 25 years or older is male and jogs is \(\boxed{0.025}\).
