Question

At a local college, 116 of the male students are smokers and 174 are no n-smokers. Of the female students, 40 are smokers and 360 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? Do not round answer

Answer 1

There are:

116 male smoker students (MS)

174 male non-smoker students (MNS)

40 female smoker students (FS)

360 female non-smoker students (FNS)

The selection of two random students, one male, and one female can be done in four different ways:

(MS)(FS) - (MS)(FNS) - (MNS)(FS) - (MNS)(FNS)

We are interested in the probability of the combination (MS)(FS), i.e., both smokers.

There is a total of 116 + 174 = 290 male students, so the probability of selecting one male smoker is:

$\begin{gathered} P(MS)=\frac{116}{290} \\ \\ \text{ Simplifying:} \\ \\ P(MS)=\frac{58}{145}=\frac{2}{5} \end{gathered}$

There are 40 + 360 = 400 female students, so the probability of selecting one female smoker is:

$\begin{gathered} P(FS)=\frac{40}{360} \\ \\ \text{ Simplifying:} \\ \\ P(FS)=\frac{1}{9} \end{gathered}$

The combined probability of both being smokers is:

$P(MS,FS)=\frac{2}{5}\cdot\frac{1}{9}=\frac{2}{45}$

The required probability is 2/45