At a local college,147 of the male students are smokers and 343 are non-smokers. Of the female students,180 are smokers and 420 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?
well, we are doing two independent studies, one on males and the other on females
p male non s = 343/490
p female non s = 420/600
so
(343/490)(420/600)
Thank you Damon
To find the probability that both the male and female students chosen for the survey are non-smokers, we need to calculate the probability of selecting a non-smoker from each group separately, and then multiply the probabilities together.
Let's begin with the probability of selecting a non-smoker male student. We know that there are 147 male smokers and 343 non-smokers. The total number of male students is the sum of smokers and non-smokers: 147 + 343 = 490.
The probability of selecting a non-smoker male student is calculated by dividing the number of non-smokers by the total number of male students: 343 / 490 ≈ 0.7.
Now let's move on to the probability of selecting a non-smoker female student. We know that there are 180 female smokers and 420 non-smokers. The total number of female students is the sum of smokers and non-smokers: 180 + 420 = 600.
The probability of selecting a non-smoker female student is calculated by dividing the number of non-smokers by the total number of female students: 420 / 600 = 0.7.
To find the probability that both a male and a female student selected are non-smokers, we multiply the probabilities of selecting a non-smoker male and a non-smoker female: 0.7 * 0.7 = 0.49.
Therefore, the probability that both a randomly selected male and female student from the college are non-smokers is 0.49 or 49%.