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(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 A total over all
All the dog: 28.
Everyone: 50.
So P of dog is 28/50.
Careful!
The bottom is everyone, 50.
Not only the other 22.
Both 28 and 50 can be divided by 2.
That makes it simpler.
So it is 14/25.
3 Check
Let's check.
The four cells add up to 50, everyone.
The table is right.
And the two cells of dog add up to its total: 8 plus 20 is 28.
So the answer is right!
Let's look back.
First: make the table.
Then: a total over all.
Last: check.