Probability and a tree diagram

Question

A study on smoking habit among students at University ABC shows that 25% of males are smokers and 4.5% of females are smokers. The sample for the study consists of 1000 students where 450 of them are males. Suppose that one students is chosen at random.

 

1. Construct a tree diagram to illustrate the situation.

2. What is the probability that the student is a smoker?

3.What is the probability that the student is a male and non-smoker?

Answer 1

1. For the tree, you just need to define the branches.  First branch can be males and females.  Second branch (under each branch) can be smokers vs non-smokers.

 

2. Looking at our tree, we see that male smokers and female smokers are mutually exclusive categories.  Probability of male smoker is probability of male (.45) times probability of smoker given a male (.25).  Calculate probability of female smoker the same way.  Then you can add these, since the categories are mutually exclusive.

 

3. Looking at our tree again, we see that probability of male non-smoker will be probability of male (.45) times probability of non-smoker given male (.75).

 

The key to understanding this is understanding the tree diagram.  If that doesn't make sense, recommend setting up a lesson so you can see it on a whiteboard.