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 0.090 (round to three decimal places as needed).

would this event be unusual? choose the correct answer

a. no, because the probability is less than 0.05.

b. yes, because the probability is less than 0.05.

c. yes, because the probability is not less than 0.05.

d. no, because the probability is not less than 0.05.

Explanation:

Step1: <Probability formula>

Use the formula \(P(A\cap B)=P(B|A)\times P(A)\). Let \(A\) be the event that a resident is a smoker and \(B\) be the event that a resident is female. Given \(P(A) = 0.2034\) and \(P(B|A)=0.4445\).

Step2: <Calculate the probability>

\(P(A\cap B)=0.4445\times0.2034 = 0.090\) (rounded to three decimal places).

Step3: <Determine if it's unusual>

An event is considered unusual if its probability is less than \(0.05\). Since \(0.090> 0.05\).

Answer:

D. No, because the probability is not less than \(0.05\)