Step by step
The question
Question: A survey asked boys and girls: art or music?
Boys: 9 art, 6 music.
Girls: 7 art, 8 music.
One person is picked at random.
Find P(boy and art).
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: 9 plus 6 is 15.
7 plus 8 is 15.
Column totals: 16 and 14.
And 30 people in all.
The totals sit at the edges, in the margins.
2 One cell over all
Boy and art: both at once.
That is one cell, 9.
Out of everyone, 30.
So P of boy and art is 9/30.
Careful!
And means out of everyone: 30.
Over 16 would be given art.
Both 9 and 30 can be divided by 3.
That makes it simpler.
So it is 3/10.
3 Check
Let's check.
The four cells add up to 30, everyone.
The table is right.
And the and rule: P of boy, 15/30, times P of art given boy, 9/15.
The 15s cancel: 9/30.
So the answer is right!
Let's look back.
First: make the table.
Then: one cell over all.
Last: check.