𝐴, 𝐵, and 𝐿 are three sets. 𝐿 is the set containing multiples
of three less than 25. 𝐴 is the set containing the
numbers six, 12, 18, and 24. And 𝐵 is the set containing the
numbers three, 12, 15, 18, and 21. Fill this information in on the
The circles on this Venn diagram
must represent the sets 𝐴 and 𝐵, since the set 𝐿 has been shown to represent the
enclosing rectangle. This set 𝐿 is sometimes called the
universal set. It represents all possible elements
that could be included.
Now we can see from the question
that sets 𝐴 and 𝐵 have the numbers 12 and 18 in common. So these numbers go in the overlap,
also called the intersection of 𝐴 and 𝐵. The remaining numbers in set 𝐴 are
six and 24. And the remaining numbers in set 𝐵
are three, 15, and 21.
Now the universal set was defined
as multiples of three less than 25. That’s essentially the three times
tables. The only number we haven’t yet used
from these multiples of three is nine. This must go outside our
circles. Once we have made sure we’ve
included all the elements of the universal set 𝐿, our Venn diagram is finished.
A number is chosen randomly from
the set 𝐿. What is the probability that the
number lies in the intersection of set 𝐴 and 𝐵? This little symbol that looks a bit
like the lowercase letter n represents the intersection of the Venn diagram.
Remember, we said the intersection
is just the overlap, the elements that are contained in both set 𝐴 and set 𝐵. There are just two numbers, 12 and
18, in this overlap. There’s a total of eight possible
numbers. The probability of choosing a
number that lies in the intersection is, therefore, two-eighths. Don’t forget to simplify your
answer. The probability that the number
chosen lies in the intersection of 𝐴 and 𝐵 is, therefore, a quarter.