Question

At a local college, 396 of the male students are smokers and 594 are non-smokers. Of the female students, 440 are smokers and 560 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 non-smokers?

Answer 1

The probability that both a randomly selected male and female student from the college are non-smokers is 33.6%.

Step-by-step explanation:

To find the probability that both a randomly selected male and female student from the college are non-smokers, we need to calculate the individual probabilities and then multiply them since these are independent events.

For the male students, 594 are non-smokers out of a total of 396 smokers + 594 non-smokers = 990 male students. Thus, the probability that a male student is a non-smoker is 594/990.

For the female students, 560 are non-smokers out of a total of 440 smokers + 560 non-smokers = 1000 female students. Hence, the probability that a female student is a non-smoker is 560/1000.

Therefore, the probability that both a randomly selected male and female student are non-smokers is:

(594/990) × (560/1000) = 0.6 × 0.56 = 0.336 or 33.6%.