10. Suppose there is a 21.3 % probability that a randomly selected person aged 2

Question

10. Suppose there is a 21.3 % probability that a randomly selected person aged 25

years or older is a jogger. In addition, there is a 12.6 % probability that a randomly selected person aged 25 years or older is male, given that he or she jogs.What is the probability that a randomly selected person aged 25 years or older is male and jogs?

Would it be unusual to randomly select a person aged 25 years or older who is male

and jogs?

The probability that a randomly selected person aged 25 years or older is male and jogs is ___?____ (Round to three decimal places as needed)

Would it be unusual?

Yes? Or No?

Explanation / Answer

Here, we are given that:

P( jogger ) = 0.213,
P( male | jogger ) = 0.126

Using bayes theorem, we get: P( male and jogger ) = P( male | jogger ) P( jogger ) = 0.213*0.126 = 0.026838

Therefore the required probability that a randomly selected person aged 25 years or older is male and jogs is 0.027. ( rounded to three decimal places )

as this probability is less than 0.05, therefore Yes it is unusual.

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