Suppose there is a 13.4 % probability that a randomly selected person aged 30 years or older is a jogger. In addition, there is a 15.4 % probability that a randomly selected person aged 30 years or older is female comma given that he or she jogs. What is the probability that a randomly selected person aged 30 years or older is female and jogs? Would it be unusual to randomly select a person aged 30 years or older who is female and jogs?

Answer: Hello mate!

if you randomly chose a 30 years or older person, there is a 13,4% (or 0.134) that he or she jogs, and if this person jogs, there is a 15,4% (or 0.154) that the person is a female.

where you can see that both probabilities are very small, and are dependent, this means that the probability 15.4% of being female only applies after the 13,4% of being a jogger.

If we want to know the probability where a randomly chosen person of 30 or older is a female and jogger, then we need to see the product of both probabilities:

this is 0.134*0.154 = 0.02

wich is equivalent to 2%, so yes, it would be very unusual to randomly select a person aged 30 years or older who is female and jogs.