Step by step
The question
Question: A survey asked juniors and seniors: bus or car?
Juniors: 18 bus, 12 car.
Seniors: 10 bus, 20 car.
One person is picked at random.
Find P(bus).
There are four choices.
First we solve it, the normal way.
Then we pick.
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: 18 plus 12 is 30.
10 plus 20 is 30.
Column totals: 28 and 32.
And 60 people in all.
The totals sit at the edges, in the margins.
2 A total over all
All the bus: 28.
Everyone: 60.
So P of bus is 28/60.
Careful!
The bottom is everyone, 60.
Not only the other 32.
Both 28 and 60 can be divided by 4.
That makes it simpler.
So it is 7/15.
3 Check
Let's check.
The four cells add up to 60, everyone.
The table is right.
And the two cells of bus add up to its total: 18 plus 10 is 28.
So the answer is right!
4 Pick the choice
Our answer is P(bus) = 7/15.
That is choice A.
5 Why not the others
B is 3/5.
Wrong: that is for the juniors only: 18 of 30.
C is 1/3.
Wrong: that is for the seniors only: 10 of 30.
D is 8/15.
Wrong: that is by car.
Let's look back.
First: make the table.
Then: a total over all.
Then: check.
Then: pick the choice.
Last: why not the others.