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 only 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.
tea only = 18 − 5 = 13
Careful!
The 5 who like both are inside the 18 too.
Start in the middle.
Careful: not tea only = 18 ✗
Coffee only: 12 minus 5 is 7.
coffee only = 12 − 5 = 7
Neither: everyone else.
30 minus 13, 5 and 7 is 5.
neither = 30 − 13 − 5 − 7 = 5
3 Find the part we want
Tea only: only one part of the circle, 13.
4 Write the fraction
So the probability is 13/30.
P(tea only) = 1330
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!
13 + 5 + 7 + 5 = 30
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.
Answer
P(tea only) = 1330