Question

according to the national center for health statistics, there is a 20.34% probability that a randomly selected resident of the united states aged 18 years or older is a smoker. in addition, there is a 44.45% probability that a randomly selected resident of the united states aged 18 years or older is female, given that they smoke. what is the probability that a randomly selected resident of the united states aged 18 years or older is female and smokes? would it be unusual to randomly select a resident of the united states aged 18 years or older who is female and smokes? the probability that a randomly selected resident of the united states aged 18 years or older is female and smokes is (round to three decimal places as needed.)

Explanation:

Step1: Identify the formula

Use the formula for conditional probability \(P(A\cap B)=P(B)\times P(A|B)\), where \(A\) is "female" and \(B\) is "smoker".

Step2: Substitute the values

Given \(P(B) = 0.2034\) and \(P(A|B)=0.4445\). Then \(P(A\cap B)=0.2034\times0.4445\).

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Step3: Round the result

Round \(0.0904113\) to three decimal places.

Answer:

\(0.090\)