36 people: 20 like pizza, 18 like pasta, 9 like both, P(pizza only)

Step by step

The question

Question: 36 people were asked.

20 like pizza, 18 like pasta, and 9 like both.

One is picked at random.

What is the probability they like only pizza?

1 Start in the middle

9 like both.

They go in the middle, where the circles overlap.

2 Fill the rest

20 like pizza, but 9 of them are already in the middle.

20 minus 9 is 11.

Careful!

The 9 who like both are inside the 20 too.

Start in the middle.

Pasta only: 18 minus 9 is 9.

Neither: everyone else.

36 minus 11, 9 and 9 is 7.

3 Find the part we want

Pizza only: only one part of the circle, 11.

4 Write the fraction

So the probability is 11/36.

5 Check

Let's check: the four parts add up to 11 plus 9 plus 9 plus 7.

That is 36, everyone.

So the answer is right!

Let's look back.

First: start in the middle.

Then: fill the rest.

Then: find the part we want.

Then: write the fraction.

Last: check.