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)=(116)/(290) \\ \\ \text{ Simplifying:} \\ \\ P(MS)=(58)/(145)=(2)/(5) \end{gathered}`

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

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

The combined probability of both being smokers is:

`P(MS,FS)=(2)/(5)\cdot(1)/(9)=(2)/(45)`

The required probability is 2/45