Question

At a local college, 138 of the male students are smokers and are non-smokers. Of the female students, are smokers and 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 the male and female student are non-smokers is 0.72.

Explanation:

The complete question is:

At a local college,178 of the male students are smokers and 712 are non-smokers. Of the female students,80 are smokers and 720 are nonsmokers. 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?

Solution:

Let, X denote the number of non-smoker male students and Y denote the number of non-smoker female students.

It is provided that:

X' = 178

X = 712

Tx = 890

Y' = 80

Y = 720

Ty = 800

Compute the probability of selecting a non-smoker male student as follows:

`P (\text{Non-smoker Male student})=(712)/(890)=0.80`

Compute the probability of selecting a non-smoker female student as follows:

`P (\text{Non-smoker Female student})=(720)/(800)=0.90`

Compute the probability that both the male and female student are non-smokers as follows:
`P(\text{Non-smoker Male and Female})=P(\text{Non-smoker Male})* P(\text{Non-smoker Female})`The event of any female student being a non-smoker is independent of the male students.

`P(\text{Non-smoker Male and Female})=0.80* 0.90`

`=0.72`

Thus, the probability that both the male and female student are non-smokers is 0.72.