Step by step
The question
Question: 30 people were asked.
18 like tea, 12 like coffee, and 5 like both.
One is picked at random.
What is the probability they like coffee, if they like tea?
1 Start in the middle
5 like both.
They go in the middle, where the circles overlap.
2 Fill the rest
18 like tea, but 5 of them are already in the middle.
18 minus 5 is 13.
Coffee only: 12 minus 5 is 7.
Neither: everyone else.
30 minus 13, 5 and 7 is 5.
3 Find the part we want
Given they like tea: only the tea circle counts.
18 in it.
Of those, 5 like coffee too.
The tea circle: 13 plus 5 is 18.
That is the new bottom.
Careful!
Given tea: the bottom is only the 18 in the tea circle.
Not all 30.
4 Write the fraction
So the probability is 5/18.
5 Check
Let's check: the four parts add up to 13 plus 5 plus 7 plus 5.
That is 30, 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.