At a local college, 297 of the male students are smokers and 693 are non-smokers. Of the female students, 310 are smokers and 690 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?Do not round your answer.
Question
At a local college, 297 of the male students are smokers and 693 are non-smokers. Of the female students, 310 are smokers and 690 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?Do not round your answer.
Solution
To find the probability that both the male and female students selected are non-smokers, we need to calculate the probability of selecting a non-smoker male student and a non-smoker female student separately, and then multiply these probabilities together.
Let's start with the probability of selecting a non-smoker male student. Out of the total number of male students, there are 693 non-smokers out of 297 smokers and 693 non-smokers. So, the probability of selecting a non-smoker male student is 693/990.
Next, let's calculate the probability of selecting a non-smoker female student. Out of the total number of female students, there are 690 non-smokers out of 310 smokers and 690 non-smokers. So, the probability of selecting a non-smoker female student is 690/1000.
To find the probability that both are non-smokers, we multiply the probability of selecting a non-smoker male student by the probability of selecting a non-smoker female student:
(693/990) * (690/1000) = 480570/990000
Therefore, the probability that both the male and female students selected are non-smokers is 480570/990000.
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