Video: Pack 2 • Paper 2 • Question 1

Pack 2 • Paper 2 • Question 1


Video Transcript

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 Venn diagram.

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.

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