Step by step
The question
Question: People were asked: tea or coffee?
6 boys chose tea and 14 chose coffee.
9 girls chose tea and 11 chose coffee.
One of the boys is picked at random.
What is the probability they chose tea?
The line means given.
Given one of the boys: we only look at the boys.
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.
6 boys chose tea, 14 chose coffee.
6 plus 14 is 20.
9 girls chose tea, 11 chose coffee.
9 plus 11 is 20.
The totals: 15 chose tea, 25 chose coffee, 40 in all.
2 Keep only the given row
Given boy: only this row counts.
The others do not.
In it: 6 chose tea, out of 20.
3 Write the fraction
So the probability is 6/20.
Careful!
The bottom is only the boys: 20.
Not all 40.
4 Simplify
Both 6 and 20 can be divided by 2.
That makes it simpler.
So it is 3/10.
5 Check
Let's check with the rule: the probability of both, divided by the probability of boy.
Both: 6 out of all 40.
Boy: 20 out of 40.
Dividing by a fraction: flip it and multiply.
The 40s cancel: 6/20.
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.