Step by step
The question
Question: People were asked: yes or no?
16 men chose yes and 4 chose no.
12 women chose yes and 8 chose no.
One of the men is picked at random.
What is the probability they chose yes?
The line means given.
Given one of the men: we only look at the men.
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.
16 men chose yes, 4 chose no.
16 plus 4 is 20.
12 women chose yes, 8 chose no.
12 plus 8 is 20.
The totals: 28 chose yes, 12 chose no, 40 in all.
2 Keep only the given row
Given man: only this row counts.
The others do not.
In it: 16 chose yes, out of 20.
3 Write the fraction
So the probability is 16/20.
Careful!
The bottom is only the men: 20.
Not all 40.
4 Simplify
Both 16 and 20 can be divided by 4.
That makes it simpler.
So it is 4/5.
5 Check
Let's check with the rule: the probability of both, divided by the probability of man.
Both: 16 out of all 40.
Man: 20 out of 40.
Dividing by a fraction: flip it and multiply.
The 40s cancel: 16/20.
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.