Question

At a local college, 267 of the male students are smokers and 623 are non-smokers. Of the female students, 500 are smokers and 500 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?

a) 267/1390
b) 267/2000
c) 500/1390
d) 500/2000

Answer 1

To find the probability that both selected students are smokers, multiply the probability of selecting a male smoker with the probability of selecting a female smoker, which results in 267/1390.

Step-by-step explanation:

The question involves finding the probability that both a male and a female student selected randomly from a college will be smokers. We can solve this by multiplying the probabilities of the two independent events: selecting a male smoker and selecting a female smoker.

First, find the total number of male students by adding the number of male smokers and non-smokers: 267 smokers + 623 non-smokers = 890. Thus, the probability of selecting a male smoker is 267/890.

For the females, the total is 500 smokers + 500 non-smokers = 1000. The probability of selecting a female smoker is 500/1000, which simplifies to 1/2.

To find the combined probability of both a male smoker and a female smoker being selected, we multiply their individual probabilities: (267/890) × (1/2) = 267/1780, which simplifies further to 267/1390 when you cancel out the common factor of 2.

Therefore, the correct answer is 267/1390.