Step by step
The question
Question: People were asked: bus or car?
8 juniors chose bus and 12 chose car.
6 seniors chose bus and 14 chose car.
One of the juniors is picked at random.
What is the probability they chose bus?
The line means given.
Given one of the juniors: we only look at the juniors.
P stands for probability.
The line stands for given.
1 Make a table
One row for each group, one column for each answer, and the totals.
8 juniors chose bus, 12 chose car.
8 plus 12 is 20.
6 seniors chose bus, 14 chose car.
6 plus 14 is 20.
The totals: 14 chose bus, 26 chose car, 40 in all.
2 Keep only the given row
Given junior: only this row counts.
The others do not.
In it: 8 chose bus, out of 20.
3 Write the fraction
So the probability is 8/20.
Careful!
The bottom is only the juniors: 20.
Not all 40.
4 Simplify
Both 8 and 20 can be divided by 4.
That makes it simpler.
So it is 2/5.
5 Check
Let's check with the rule: the probability of both, divided by the probability of junior.
Both: 8 out of all 40.
Junior: 20 out of 40.
Dividing by a fraction: flip it and multiply.
The 40s cancel: 8/20.
The same.
So the answer is right!
Let's look back.
First: make a table.
Then: keep only the given row.
Then: write the fraction.
Then: simplify.
Last: check.