Question

Suppose there is a 14.3% probability that a randomly selected person aged 25 years or older is a In​ addition, there is a probability that a randomly selected person aged years or older is given that he or she What is the probability that a randomly selected person aged years or older is and Would it be unusual to randomly select a person aged years or older who is and

Answer 1

Complete Question

Suppose there is a 14.3% probability that a randomly selected person aged 25 years or older is a jogger. In addition, there is a 52.6% probability that a randomly selected person aged 25 years or older is female, given that he or she jogs. What is the probability that a randomly selected person aged 25 years or older is female and jogs? Would it be unusual to randomly select a person aged 25 years or older who is female and jogs?

Answer:

The  probability is  $P(F \ n \ J ) = 0.075$

No  it is not unusual

Step-by-step explanation:

From the question we are told that

The probability  that a  randomly selected person aged 25 or older is a jogger  is

     $P(J) = 0.143$

The probability that a randomly selected person aged 25 years or older is female, given that he or she jogs

     $P(F | J) = 0.526$

Generally the  the probability that a randomly selected person aged 25 years or older is female and jogs is mathematically evaluated using Bayes rules as follows

       $P(F \ n \ J ) = P(F | J ) * P(J )$

=>    $P(F \ n \ J ) = 0.526 * 0.143$

=>    $P(F \ n \ J ) = 0.075$

Generally this is not unusual  because value obtained is greater than 0.05