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: Calculate total male students

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

Step2: Calculate total female students

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

Step3: Probability male is smoker

Probability that a randomly selected male is a smoker, \(P(M)=\frac{164}{410}\)

Step4: Probability female is smoker

Probability that a randomly selected female is a smoker, \(P(F)=\frac{60}{300}\)

Step5: Probability both are smokers

Since the selection of male and female are independent events, the probability that both are smokers is \(P(M)\times P(F)=\frac{164}{410}\times\frac{60}{300}\)
Simplify \(\frac{164}{410}\times\frac{60}{300}=\frac{164\times60}{410\times300}=\frac{9840}{123000}=\frac{82}{1025}\) (after simplifying the fraction by dividing numerator and denominator by 120)

Answer:

\(\frac{82}{1025}\)