Question

at a local college, 164 of the male students are smokers and 246 are non - smokers. of the female students, 60 are smokers and 240 are non - smokers. a male student and a female student from the college are randomly selected for a survey. what is the probability that both are smokers? do not round your answer. (if necessary, consult a list of formulas.)

Explanation:

Step1: Find total male students

Total male students = smokers + non - smokers = \(164 + 246=410\)

Step2: Find total female students

Total female students = smokers + non - smokers = \(60+240 = 300\)

Step3: Probability male is smoker

Probability (male smoker) = \(\frac{\text{male smokers}}{\text{total male students}}=\frac{164}{410}\)

Step4: Probability female is smoker

Probability (female smoker) = \(\frac{\text{female smokers}}{\text{total female students}}=\frac{60}{300}\)

Step5: Probability both are smokers

Since the selection of male and female are independent events, we multiply the two probabilities.
\(P(\text{both smokers})=\frac{164}{410}\times\frac{60}{300}\)
Simplify \(\frac{164}{410}=\frac{82}{205}=\frac{2}{5}\) (dividing numerator and denominator by 41) and \(\frac{60}{300}=\frac{1}{5}\)
Then \(P(\text{both smokers})=\frac{2}{5}\times\frac{1}{5}=\frac{2}{25}\) (or we can calculate directly: \(\frac{164\times60}{410\times300}=\frac{9840}{123000}=\frac{9840\div4920}{123000\div4920}=\frac{2}{25}\))

Answer:

\(\frac{2}{25}\)