Step by step
The question
Question: People were asked: yes or no?
5 boys chose yes and 15 chose no.
10 girls chose yes and 10 chose no.
One of the girls is picked at random.
What is the probability they chose yes?
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.
5 boys chose yes, 15 chose no.
5 plus 15 is 20.
10 girls chose yes, 10 chose no.
10 plus 10 is 20.
The totals: 15 chose yes, 25 chose no, 40 in all.
2 Keep only the given row
Given girl: only this row counts.
The others do not.
In it: 10 chose yes, out of 20.
3 Write the fraction
So the probability is 10/20.
Careful!
The bottom is only the girls: 20.
Not all 40.
4 Simplify
Both 10 and 20 can be divided by 10.
That makes it simpler.
So it is 1/2.
5 Check
Let's check with the rule: the probability of both, divided by the probability of girl.
Both: 10 out of all 40.
Girl: 20 out of 40.
Dividing by a fraction: flip it and multiply.
The 40s cancel: 10/20.
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.