Step by step
The question
Question: 50 students were asked.
28 take art, 20 take music, and 10 take both.
One is picked at random.
What is the probability they take art, if they take music?
1 Start in the middle
10 take both.
They go in the middle, where the circles overlap.
2 Fill the rest
28 take art, but 10 of them are already in the middle.
28 minus 10 is 18.
Music only: 20 minus 10 is 10.
Neither: everyone else.
50 minus 18, 10 and 10 is 12.
3 Find the part we want
Given they take music: only the music circle counts.
20 in it.
Of those, 10 take art too.
The music circle: 10 plus 10 is 20.
That is the new bottom.
Careful!
Given music: the bottom is only the 20 in the music circle.
Not all 50.
4 Write the fraction
So the probability is 10/20.
Both 10 and 20 can be divided by 10.
That makes it simpler.
So it is 1/2.
5 Check
Let's check: the four parts add up to 18 plus 10 plus 10 plus 12.
That is 50, 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.