Step by step
The question
Question: A survey asked adults and children: tea or coffee?
Adults: 30 tea, 10 coffee.
Children: 5 tea, 15 coffee.
One person is picked at random.
Find P(child and coffee).
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: 30 plus 10 is 40.
5 plus 15 is 20.
Column totals: 35 and 25.
And 60 people in all.
The totals sit at the edges, in the margins.
2 One cell over all
Child and coffee: both at once.
That is one cell, 15.
Out of everyone, 60.
So P of child and coffee is 15/60.
Careful!
And means out of everyone: 60.
Over 25 would be given coffee.
Both 15 and 60 can be divided by 15.
That makes it simpler.
So it is 1/4.
3 Check
Let's check.
The four cells add up to 60, everyone.
The table is right.
And the and rule: P of child, 20/60, times P of coffee given child, 15/20.
The 20s cancel: 15/60.
So the answer is right!
Let's look back.
First: make the table.
Then: one cell over all.
Last: check.