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(car) and P(senior and car).
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 car: 26.
Everyone: 40.
So P of car is 26/40.
Careful!
The bottom is everyone, 40.
Not only the other 14.
Both 26 and 40 can be divided by 2.
So it is 13/20.
3 One cell over all
Senior and car: both at once.
That is one cell, 14.
Out of everyone, 40.
So P of senior and car is 14/40.
Both 14 and 40 can be divided by 2.
So it is 7/20.
So: P of car is 13/20.
P of senior and car is 7/20.
4 Check
Let's check.
The four cells add up to 40, everyone.
The table is right.
And the two cells of car add up to its total: 12 plus 14 is 26.
So the answer is right!
Let's look back.
First: make the table.
Then: a total over all.
Then: one cell over all.
Last: check.