Question

Suppose there is a 27.4% probability that a randomly selected person aged 40 years or older is a jogger. In addition, there is a 29.3% probability that a randomly selected person age 40 years or older is male, given that he or she jogs.

Required:
a. What is the probability that a randomly selected person age 40 years or older is male and jogs?
b. Would it be unusual to randomly select a person aged 40 years or older who is male and jogs?

Answer 1

a

`P(M  \  n \  J ) = 0.0802`

b

Yes

Explanation:

From the question we are told that

The probability that a random selected person of age 40 years or older is a jogger is
`P(J) =  0.274`

The probability that a random selected person of age 40 years or older is a male given that he/she jogs is
`P(M |J) = 0.293`

Generally the probability that a randomly selected person age 40 years or older is male and jogs

`P(M  \  n \  J ) = P(M|J) *  P(J)`

`P(M  \  n \  J ) = 0.293 * 0.274`

`P(M  \  n \  J ) = 0.0802`

Generally it would be unusual because the probability that a randomly selected person age 40 years or older is male and jogs is greater than 0.05[border line for statistical significance]