Question

Suppose there is a 26.2% probability that a randomly selected person aged 20 years or older is a jogger. In addition, there is a 10.2% probability that arandomly selected person aged 20 years or older is male, given that he or she jogs. What is the probability that a randomly selected person aged 20years or older is male and jogs? Would it be unusual to randomly select a person aged 20 years or older who is male and jogs?The probability that a randomly selected person aged 20 years or older is male and jogs is(Round to three decimal places as needed.)

Answer 1

P(J∩M) = 0.027

Step-by-step explanation:

Let's call J the event that a selected person aged 20 years or older is a jogger and M the event that a selected person aged 20 years or older is male.

Then, the probability P(J∩M) that a randomly selected person aged 20

years or older is male and jogs can be calculated as:

P(J∩M) = P(J) * P(M|J)

Where P(J) is the probability that a selected person aged 20 years or older is a jogger and P(M|J) is the probability that hat a selected person aged 20 years or older is male given that he or she jogs.

So, replacing P(J) by 26.2% and P(M|J) by 10.2%, we get:

P(J∩M) = 0.262 * 0.102

P(J∩M) = 0.027

P(J∩M) = 2.7%

Therefore, the probability that a randomly selected person aged 20 years or older is male and jogs is 0.027