Question

At a local college, 82 of the male students are smokers and 328 are non-smokers. Of the female students, 148 are smokers and 252 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?

Answer 1

Let's start by calculating the probability that a male student is a smoker:

P(male smoker) = 82 / (82 + 328) = 0.20

Similarly, the probability that a female student is a smoker is:

P(female smoker) = 148 / (148 + 252) = 0.37

To calculate the probability that both are smokers, we need to multiply these probabilities:

P(both smokers) = P(male smoker) x P(female smoker)
P(both smokers) = 0.20 x 0.37
P(both smokers) = 0.074

Therefore, the probability that both a male and a female student selected at random from the college are smokers is 0.074, or approximately 7.4%.