The whole red circle C contains the percentage of all people
who own a cell phone.
The whole blue circle L contains the percentage of all people who
own a laptop.
The red circle consists of the regions indicated by a and b.
The blue circle consists of the regions indicated by b and c.
The region indicated by b represent the percentage of people
who own both a cell phone and a laptop.
We look at the most inclusive clue first:
40% own both.
Those who own both are represented by the region marked b, the
region where both circles overlap. So we put 40% in that middle
region where the circles overlap:
Next we look at this clue:
75% of households own a cell phone
This is the entire red circle C. It already contains 40% in
the part that overlaps the blue circle. So to determine what
percentage goes in region a, we subtract 75%-40% and get 35%
to go in the region a:
Next we look at this clue:
45% own a laptop
This is the entire blue circle L. It already contains 40% in
the part that overlaps the red circle. So to determine what
percentage goes in region c, we subtract 45%-40% and get 5%
to go in the region c:
So far we have that:
30% own a cell phone but do not own a laptop.
40% own both a cell phone and a laptop.
5% own a laptop but do not own a cell phone.
But some people do not own either. They are in the region
inside the big rectangle but outside of both circles, indicated
by the letter d.
To find out what percent goes in this outer region d, we add what the
percents in the three regions we have already filled in:
30% + 40% + 5 % = 75%
and subtract from 100%
100% - 75% = 25%.
So we put 25% in the outside region marked d:
B) determine the probability that a randomly selected person owns
a laptop or a cell phone.
We just add the three percentages inside the circles (which we
already did above to calculate the 25%).
30% + 40% + 5 % = 75%
Edwin