Step by step
The question
Question: A survey asked boys and girls: cat or dog?
Boys: 12 cat, 8 dog.
Girls: 10 cat, 20 dog.
One person is picked at random.
Find P(girl or dog).
1 Make the table
One row for each group, one column for each answer, and a total for each.
The four counts go inside.
Row totals: 12 plus 8 is 20.
10 plus 20 is 30.
Column totals: 22 and 28.
And 50 people in all.
The totals sit at the edges, in the margins.
2 Add, take away the overlap
Girl: 30.
Dog: 28.
But 20 are both.
They are in both totals.
The or rule: add the two, then take away the overlap, so it is counted once.
Careful!
Without taking away 20, the people who are both are counted twice.
Same bottoms: 30 plus 28 minus 20 is 38.
So it is 38/50.
Both 38 and 50 can be divided by 2.
That makes it simpler.
So it is 19/25.
3 Check
Let's check.
The four cells add up to 50, everyone.
The table is right.
And count straight from the table: all 30 girls, plus the 8 others who chose dog.
That is 38.
So the answer is right!
Let's look back.
First: make the table.
Then: add, take away the overlap.
Last: check.