Step by step
The question
Question: A survey asked men and women: walk or drive?
Men: 14 walk, 6 drive.
Women: 9 walk, 11 drive.
One person is picked at random.
Find P(man or walk).
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: 14 plus 6 is 20.
9 plus 11 is 20.
Column totals: 23 and 17.
And 40 people in all.
The totals sit at the edges, in the margins.
2 Add, take away the overlap
Man: 20.
Walk: 23.
But 14 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 14, the people who are both are counted twice.
Same bottoms: 20 plus 23 minus 14 is 29.
So it is 29/40.
3 Check
Let's check.
The four cells add up to 40, everyone.
The table is right.
And count straight from the table: all 20 men, plus the 9 others who chose walk.
That is 29.
So the answer is right!
Let's look back.
First: make the table.
Then: add, take away the overlap.
Last: check.