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 [tex]P(F \ n \ J ) = 0.075[/tex]
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
[tex]P(J) = 0.143[/tex]
The probability that a randomly selected person aged 25 years or older is female, given that he or she jogs
[tex]P(F | J) = 0.526[/tex]
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
[tex]P(F \ n \ J ) = P(F | J ) * P(J )[/tex]
=> [tex]P(F \ n \ J ) = 0.526 * 0.143[/tex]
=> [tex]P(F \ n \ J ) = 0.075[/tex]
Generally this is not unusual because value obtained is greater than 0.05
