At a local college, 81 of the male students are smokers and 729 are non-smokers. Of the female students, 350 are smokers and 350 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 the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

81/(729+81) * 350/(350+350) = ?

To find the probability that both the male and female students are smokers, we need to calculate the probability of selecting a smoker from both groups and then multiply them together.

Let's start by finding the probability of selecting a smoker from the male students. We have been given that there are 81 male smokers out of a total of 81 (smokers) + 729 (non-smokers) = 810 male students. Therefore, the probability of selecting a male smoker is 81/810 = 0.1.

Next, let's find the probability of selecting a smoker from the female students. We are given that there are 350 female smokers out of a total of 350 (smokers) + 350 (non-smokers) = 700 female students. Therefore, the probability of selecting a female smoker is 350/700 = 0.5.

To find the probability that both the male and female students are smokers, we multiply the two probabilities together:
P(both are smokers) = P(male smoker) * P(female smoker)
= 0.1 * 0.5
= 0.05

Therefore, the probability that both the selected male and female students are smokers is 0.05.