Step by step
The question
Question: People were asked: yes or no?
18 men chose yes and 6 chose no.
14 women chose yes and 12 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.
18 men chose yes, 6 chose no.
18 plus 6 is 24.
14 women chose yes, 12 chose no.
14 plus 12 is 26.
The totals: 32 chose yes, 18 chose no, 50 in all.
2 Keep only the given row
Given man: only this row counts.
The others do not.
In it: 18 chose yes, out of 24.
3 Write the fraction
So the probability is 18/24.
Careful!
The bottom is only the men: 24.
Not all 50.
4 Simplify
Both 18 and 24 can be divided by 6.
That makes it simpler.
So it is 3/4.
5 Check
Let's check with the rule: the probability of both, divided by the probability of man.
Both: 18 out of all 50.
Man: 24 out of 50.
Dividing by a fraction: flip it and multiply.
The 50s cancel: 18/24.
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.