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 person who chose car is picked at random.
What is the probability they are one of the seniors?
The line means given.
Given they chose car: we only look at the people who chose car.
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 column
Given car: only this column counts.
The others do not.
In it: 14 are seniors, out of 26.
3 Write the fraction
So the probability is 14/26.
Careful!
The bottom is only the people who chose car: 26.
Not all 40.
4 Simplify
Both 14 and 26 can be divided by 2.
That makes it simpler.
So it is 7/13.
5 Check
Let's check with the rule: the probability of both, divided by the probability of car.
Both: 14 out of all 40.
Car: 26 out of 40.
Dividing by a fraction: flip it and multiply.
The 40s cancel: 14/26.
The same.
So the answer is right!
Let's look back.
First: make a table.
Then: keep only the given column.
Then: write the fraction.
Then: simplify.
Last: check.