Question

Suppose there is a 13.9 % probability that a randomly selected person aged 40 years or older is a jogger. In​ addition, there is a 15.6 % probability that a randomly selected person aged 40 years or older is male comma given that he or she jogs. What is the probability that a randomly selected person aged 40 years or older is male and jogs question mark Would it be unusual to randomly select a person aged 40 years or older who is male and jogs question mark The probability that a randomly selected person aged 40 years or older is male and jogs is nothing ​(Round to three decimal places as​ needed.).

Answer 1

Answer:

There is a 2.17% probability that a randomly selected person aged 40 years or older is male and jogs.

It would be unusual to randomly select a person aged 40 years or older who is male and jogs.

Step-by-step explanation:

We have these following probabilities.

A 13.9% probability that a randomly selected person aged 40 years or older is a jogger, so $P(A) = 0.13$.

In​ addition, there is a 15.6% probability that a randomly selected person aged 40 years or older is male comma given that he or she jogs. I am going to say that P(B) is the probability that is a male. $P(B/A)$ is the probability that the person is a male, given that he/she jogs. So $P(B/A) = 0.156$

The Bayes theorem states that:

$P(B/A) = \frac{P(A \cap B)}{P(A)}$

In which $P(A \cap B)$ is the probability that the person does both thigs, so, in this problem, the probability that a randomly selected person aged 40 years or older is male and jogs.

So

$P(A \cap B) = P(A).P(B/A) = 0.156*0.139 = 0.217$

There is a 2.17% probability that a randomly selected person aged 40 years or older is male and jogs.

A probability is unusual when it is smaller than 5%.

So it would be unusual to randomly select a person aged 40 years or older who is male and jogs.