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 person who chose tea is picked at random.
What is the probability they are one of the adults?
The line means given.
Given they chose tea: we only look at the people who chose tea.
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 column
Given tea: only this column counts.
The others do not.
In it: 30 are adults, out of 35.
3 Write the fraction
So the probability is 30/35.
Careful!
The bottom is only the people who chose tea: 35.
Not all 60.
4 Simplify
Both 30 and 35 can be divided by 5.
That makes it simpler.
So it is 6/7.
5 Check
Let's check with the rule: the probability of both, divided by the probability of tea.
Both: 30 out of all 60.
Tea: 35 out of 60.
Dividing by a fraction: flip it and multiply.
The 60s cancel: 30/35.
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.