40 students: 22 play soccer, 15 play tennis, 8 play both, P(both)

Step by step

The question

Question: 40 students were asked.

22 play soccer, 15 play tennis, and 8 play both.

One is picked at random.

What is the probability they play both?

1 Start in the middle

8 play both.

They go in the middle, where the circles overlap.

2 Fill the rest

22 play soccer, but 8 of them are already in the middle.

22 minus 8 is 14.

Tennis only: 15 minus 8 is 7.

Neither: everyone else.

40 minus 14, 8 and 7 is 11.

3 Find the part we want

Both: the middle, 8.

4 Write the fraction

So the probability is 8/40.

Both 8 and 40 can be divided by 8.

That makes it simpler.

So it is 1/5.

5 Check

Let's check: the four parts add up to 14 plus 8 plus 7 plus 11.

That is 40, 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.