Step by step
The question
Question: People were asked: bike or walk?
15 boys chose bike and 25 chose walk.
20 girls chose bike and 20 chose walk.
One person who chose bike is picked at random.
What is the probability they are one of the girls?
The line means given.
Given they chose bike: we only look at the people who chose bike.
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.
15 boys chose bike, 25 chose walk.
15 plus 25 is 40.
20 girls chose bike, 20 chose walk.
20 plus 20 is 40.
The totals: 35 chose bike, 45 chose walk, 80 in all.
2 Keep only the given column
Given bike: only this column counts.
The others do not.
In it: 20 are girls, out of 35.
3 Write the fraction
So the probability is 20/35.
Careful!
The bottom is only the people who chose bike: 35.
Not all 80.
4 Simplify
Both 20 and 35 can be divided by 5.
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 bike.
Both: 20 out of all 80.
Bike: 35 out of 80.
Dividing by a fraction: flip it and multiply.
The 80s cancel: 20/35.
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.