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 tennis, if they play soccer?
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
Given they play soccer: only the soccer circle counts.
22 in it.
Of those, 8 play tennis too.
The soccer circle: 14 plus 8 is 22.
That is the new bottom.
Careful!
Given soccer: the bottom is only the 22 in the soccer circle.
Not all 40.
4 Write the fraction
So the probability is 8/22.
Both 8 and 22 can be divided by 2.
That makes it simpler.
So it is 4/11.
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.