Step by step
The question
Question: People were asked: cat or dog?
12 boys chose cat and 8 chose dog.
10 girls chose cat and 20 chose dog.
One of the girls is picked at random.
What is the probability they chose dog?
The line means given.
Given one of the girls: we only look at the girls.
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.
12 boys chose cat, 8 chose dog.
12 plus 8 is 20.
10 girls chose cat, 20 chose dog.
10 plus 20 is 30.
The totals: 22 chose cat, 28 chose dog, 50 in all.
2 Keep only the given row
Given girl: only this row counts.
The others do not.
In it: 20 chose dog, out of 30.
3 Write the fraction
So the probability is 20/30.
Careful!
The bottom is only the girls: 30.
Not all 50.
4 Simplify
Both 20 and 30 can be divided by 10.
That makes it simpler.
So it is 2/3.
5 Check
Let's check with the rule: the probability of both, divided by the probability of girl.
Both: 20 out of all 50.
Girl: 30 out of 50.
Dividing by a fraction: flip it and multiply.
The 50s cancel: 20/30.
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.