Step by step
The question
Question: 32 students were asked.
20 study french, 15 study spanish, and 6 study both.
One is picked at random.
What is the probability they study only french?
1 Start in the middle
The box is all 32 students.
One circle for french.
One circle for spanish.
6 study both.
They go in the middle, where the circles overlap.
2 Fill the rest
20 study french, but 6 of them are already in the middle.
20 minus 6 is 14.
Careful!
The 6 who study both are inside the 20 too.
Start in the middle.
The right way: french only = 20 − 6 = 14.
Spanish only: 15 minus 6 is 9.
Neither: everyone else.
32 minus 14, 6 and 9 is 3.
3 Find the part we want
French only: only one part of the circle, 14.
4 Write the fraction
So the probability is 14/32.
Both 14 and 32 can be divided by 2.
That makes it simpler.
So it is 7/16.
5 Check
Let's check: the four parts add up to 14 plus 6 plus 9 plus 3.
That is 32, 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.