Question

suppose there is a 22.5% probability that a randomly - selected person aged 20 years or older is a smoker. in addition, there is a 11.2% probability that a randomly - selected person aged 20 years or older is female, given that the person smokes. what is the probability that a randomly - selected person aged 20 years or older is female and smokes? would it be unusual to randomly select a person aged 20 years or older who is female and smokes?
the probability that a randomly - selected person aged 20 years or older is female and smokes is 0.025 (round to three decimal places as needed.)
would it be unusual?
yes
no

Explanation:

Step1: Identify given probabilities

Let $P(S)$ be the probability of being a smoker. $P(S)=0.225$. Let $P(F|S)$ be the probability of being female given that the person is a smoker. $P(F|S) = 0.112$.

Step2: Use the formula for conditional - probability

The formula for conditional probability is $P(F|S)=\frac{P(F\cap S)}{P(S)}$. We want to find $P(F\cap S)$. Rearranging the formula gives $P(F\cap S)=P(F|S)\times P(S)$.

Step3: Calculate the probability

Substitute the given values into the formula: $P(F\cap S)=0.112\times0.225 = 0.0252$.

Answer:

$0.025$