Step by step
The question
Question: 25 people were asked.
12 own cats, 10 own dogs, and 4 own both.
One is picked at random.
What is the probability they own only dogs?
1 Start in the middle
4 own both.
They go in the middle, where the circles overlap.
2 Fill the rest
12 own cats, but 4 of them are already in the middle.
12 minus 4 is 8.
cats only = 12 − 4 = 8
Dogs only: 10 minus 4 is 6.
dogs only = 10 − 4 = 6
Careful!
The 4 who own both are inside the 10 too.
Start in the middle.
Careful: not dogs only = 10 ✗
Neither: everyone else.
25 minus 8, 4 and 6 is 7.
neither = 25 − 8 − 4 − 6 = 7
3 Find the part we want
Dogs only: only one part of the circle, 6.
4 Write the fraction
So the probability is 6/25.
P(dogs only) = 625
5 Check
Let's check: the four parts add up to 8 plus 4 plus 6 plus 7.
That is 25, everyone.
So the answer is right!
8 + 4 + 6 + 7 = 25
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(dogs only) = 625