Step by step
The question
Question: People were asked: indoor or outdoor?
14 cats chose indoor and 6 chose outdoor.
4 dogs chose indoor and 16 chose outdoor.
One person who chose indoor is picked at random.
What is the probability they are one of the cats?
The line means given.
Given they chose indoor: we only look at the people who chose indoor.
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.
14 cats chose indoor, 6 chose outdoor.
14 plus 6 is 20.
4 dogs chose indoor, 16 chose outdoor.
4 plus 16 is 20.
The totals: 18 chose indoor, 22 chose outdoor, 40 in all.
2 Keep only the given column
Given indoor: only this column counts.
The others do not.
In it: 14 are cats, out of 18.
3 Write the fraction
So the probability is 14/18.
Careful!
The bottom is only the people who chose indoor: 18.
Not all 40.
4 Simplify
Both 14 and 18 can be divided by 2.
That makes it simpler.
So it is 7/9.
5 Check
Let's check with the rule: the probability of both, divided by the probability of indoor.
Both: 14 out of all 40.
Indoor: 18 out of 40.
Dividing by a fraction: flip it and multiply.
The 40s cancel: 14/18.
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.