Step by step
The question
Question: People were asked: tea or coffee?
30 adults chose tea and 10 chose coffee.
5 children chose tea and 15 chose coffee.
One of the adults is picked at random.
What is the probability they chose coffee?
The line means given.
Given one of the adults: we only look at the adults.
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.
30 adults chose tea, 10 chose coffee.
30 plus 10 is 40.
5 children chose tea, 15 chose coffee.
5 plus 15 is 20.
The totals: 35 chose tea, 25 chose coffee, 60 in all.
2 Keep only the given row
Given adult: only this row counts.
The others do not.
In it: 10 chose coffee, out of 40.
3 Write the fraction
So the probability is 10/40.
Careful!
The bottom is only the adults: 40.
Not all 60.
4 Simplify
Both 10 and 40 can be divided by 10.
That makes it simpler.
So it is 1/4.
5 Check
Let's check with the rule: the probability of both, divided by the probability of adult.
Both: 10 out of all 60.
Adult: 40 out of 60.
Dividing by a fraction: flip it and multiply.
The 60s cancel: 10/40.
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.