Question

At a local college, 19 of the male students are smokers and 171 are non-smokers. Of the female students, 40 are smokers and 60 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?

Answer 1

0.2 or 20%

Explanation:

To find the probability that both the male student and the female student are smokers, we need to consider the probabilities of each event separately and then multiply them together.

Let's define the events:

A: Selecting a male student who is a smoker

B: Selecting a female student who is a smoker

We are given the following information:

Number of male students who are smokers (event A): 19

Total number of male students (smokers + non-smokers): 19 + 171 = 190

Number of female students who are smokers (event B): 40

Total number of female students (smokers + non-smokers): 40 + 60 = 100

Now, we can calculate the probabilities of each event:

`P(A) = \frac{\text{Number of male smokers}}{\text{Total number of male students}} = (19)/(190)`

`P(B) = \frac{\text{Number of female smokers}}{\text{Total number of female students}} = (40)/(100)`

To find the probability that both are smokers, we multiply the probabilities of event A and event B:

`P(\text{Both are smokers}) = P(A) * P(B) = (19)/(190) * (40)/(100)`

Now, let's calculate the probability:

`P(\text{Both are smokers}) = (19)/(190) * (40)/(100) = (38)/(190) = 0.2`

So, the probability that both the male student and the female student are smokers is 0.2 or 20%.