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 of the women is picked at random.
What is the probability they chose no?
The line means given.
Given one of the women: we only look at the women.
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 row
Given woman: only this row counts.
The others do not.
In it: 22 chose no, out of 40.
3 Write the fraction
So the probability is 22/40.
Careful!
The bottom is only the women: 40.
Not all 80.
4 Simplify
Both 22 and 40 can be divided by 2.
That makes it simpler.
So it is 11/20.
5 Check
Let's check with the rule: the probability of both, divided by the probability of woman.
Both: 22 out of all 80.
Woman: 40 out of 80.
Dividing by a fraction: flip it and multiply.
The 80s cancel: 22/40.
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.