Step by step
The question
Question: People were asked: art or music?
9 boys chose art and 6 chose music.
7 girls chose art and 8 chose music.
One person who chose music is picked at random.
What is the probability they are one of the boys?
The line means given.
Given they chose music: we only look at the people who chose music.
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.
9 boys chose art, 6 chose music.
9 plus 6 is 15.
7 girls chose art, 8 chose music.
7 plus 8 is 15.
The totals: 16 chose art, 14 chose music, 30 in all.
2 Keep only the given column
Given music: only this column counts.
The others do not.
In it: 6 are boys, out of 14.
3 Write the fraction
So the probability is 6/14.
Careful!
The bottom is only the people who chose music: 14.
Not all 30.
4 Simplify
Both 6 and 14 can be divided by 2.
That makes it simpler.
So it is 3/7.
5 Check
Let's check with the rule: the probability of both, divided by the probability of music.
Both: 6 out of all 30.
Music: 14 out of 30.
Dividing by a fraction: flip it and multiply.
The 30s cancel: 6/14.
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.