Step by step
The question
Question: A survey asked juniors and seniors: bus or car?
Juniors: 8 bus, 12 car.
Seniors: 6 bus, 14 car.
One person is picked at random.
Find P(junior).
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: 8 plus 12 is 20.
6 plus 14 is 20.
Column totals: 14 and 26.
And 40 people in all.
The totals sit at the edges, in the margins.
2 A total over all
All the juniors: 20.
Everyone: 40.
So P of junior is 20/40.
Careful!
The bottom is everyone, 40.
Not only the other 20.
Both 20 and 40 can be divided by 20.
That makes it simpler.
So it is 1/2.
3 Check
Let's check.
The four cells add up to 40, everyone.
The table is right.
And the two cells of junior add up to its total: 8 plus 12 is 20.
So the answer is right!
Let's look back.
First: make the table.
Then: a total over all.
Last: check.