Suppose there is a 17.5 % probability that a randomly selected person aged 35 years or older is a smoker. In​ addition, there is a 25.5 % probability that a randomly selected person aged 35 years or older is female comma given that he or she smokes.

What is the probability that a randomly selected person aged 35 years or older is female and smokes?
Would it be unusual to randomly select a person aged 35 years or older who is female and smokes ?

a)  P(U and T) = 0.045

b) YES!, a randomly selected person aged 35 years and older is a female and smokes are an unusual.

Step-by-step explanation:

Let T represents the event that the randomly selected person is a smoker

Let U represents the event that the randomly selected person is female.

Given that; there is a 17.5% probability that a randomly selected person agef 35 years or older is a smoker.

i.e P(T) = 0.175

and there is a 25.5% probability that a randomly selected person aged 35 years or older is a female, given that he or she smokes.

i.e P (U|T) = 0.255

Then;

P (U|T) =

0.255 =

P(U and T) = 0,255 × 0.175

P(U and T) = 0.044625

P(U and T) = 0.045

∴ The probability that a randomly selected person aged 35 years or older is female and smokes is 0.045

b)

The probability that a randomly selected person aged 35 years or older is female and smokes is 0.045.

It is seen that the probability is less than 0.05; thus illustrating that the randomly selected person aged 35 years or older is female and smokes is an unusual event.

∴ YES!, a randomly selected person aged 35 years and older is a female and smokes are an unusual.