EXAMPLE 3.4.1 SOLUTIONS

As with counting problems, when a probability problem refers to two overlapping categories, we can organize the information with a Venn diagram.

Since the data was given in terms of percentages, we pretend that the total population is 100. Then, each of the percentages is just a raw number.

1. The number of cowboys who have saddle sores or bowed legs = 23 + 40 + 12 = 75.

So, P(saddle sores or bowed legs) = 75/100 = .75

2. From the diagram, the number of cowboys who don't have saddle sores is

12 + 25 = 37, so

P(doesn't have saddle sores) = 37/100 = .37

We could also get this answer from the complements rule. Since 63% of the cowboys have saddle sores, P(has saddle sores) = .63.

Then, P(don't have saddle sores) = 1 - .63 = .37.

3. The diagram shows us that there are 23 cowboys out of 100 who have saddle sores but don't have bowed legs, so P(has saddle sores but not bowed legs) = 23/100 = .23

4. The diagram shows that 40 cowboys out of 100 have both conditions (this information was also stated directly at the beginning of the problem), so

P(has saddle sores and bowed legs) = 40/100 = .40

5. The diagram shows that there are 25 cowboys out of 100 who have neither affliction, so

P(has neither affliction) = 25/100 = .25