Step by step
The question
Question: A survey asked men and women: left or right?
Men: 20 left, 5 right.
Women: 10 left, 15 right.
One person is picked at random.
Find P(woman or right).
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: 20 plus 5 is 25.
10 plus 15 is 25.
Column totals: 30 and 20.
And 50 people in all.
The totals sit at the edges, in the margins.
2 Add, take away the overlap
Woman: 25.
Right: 20.
But 15 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 15, the people who are both are counted twice.
Same bottoms: 25 plus 20 minus 15 is 30.
So it is 30/50.
Both 30 and 50 can be divided by 10.
That makes it simpler.
So it is 3/5.
3 Check
Let's check.
The four cells add up to 50, everyone.
The table is right.
And count straight from the table: all 25 women, plus the 5 others who chose right.
That is 30.
So the answer is right!
Let's look back.
First: make the table.
Then: add, take away the overlap.
Last: check.