Step by step
The question
Question: People were asked: yes or no?
24 men chose yes and 16 chose no.
18 women chose yes and 22 chose no.
One person who chose yes is picked at random.
What is the probability they are one of the men?
The line means given.
Given they chose yes: we only look at the people who chose yes.
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.
24 men chose yes, 16 chose no.
24 plus 16 is 40.
18 women chose yes, 22 chose no.
18 plus 22 is 40.
The totals: 42 chose yes, 38 chose no, 80 in all.
2 Keep only the given column
Given yes: only this column counts.
The others do not.
In it: 24 are men, out of 42.
3 Write the fraction
So the probability is 24/42.
Careful!
The bottom is only the people who chose yes: 42.
Not all 80.
4 Simplify
Both 24 and 42 can be divided by 6.
That makes it simpler.
So it is 4/7.
5 Check
Let's check with the rule: the probability of both, divided by the probability of yes.
Both: 24 out of all 80.
Yes: 42 out of 80.
Dividing by a fraction: flip it and multiply.
The 80s cancel: 24/42.
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.