Question

suppose there is a 22.3% 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 probability formula

Use the formula for conditional - probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$, where $A$ is the event of being female and $B$ is the event of being a smoker. We want to find $P(A\cap B)$, and we know $P(B) = 0.223$ and $P(A|B)=0.112$.

Step2: Rearrange the formula

From $P(A|B)=\frac{P(A\cap B)}{P(B)}$, we can get $P(A\cap B)=P(A|B)\times P(B)$.

Step3: Calculate the probability

Substitute the given values: $P(A\cap B)=0.112\times0.223 = 0.025$.

Step4: Determine if it's unusual

An event is considered unusual if its probability is less than or equal to 0.05. Since $0.025\leq0.05$, it is unusual.

Answer:

The probability that a randomly - selected person aged 20 years or older is female and smokes is 0.025.
Yes