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Represent these sets on the Venn diagram - Junior Cycle Mathematics - Question (a) - 2013

Question (a)

Represent these sets on the Venn diagram. $U = \{1, 2, 3, \ldots, 12\}$ $P$ is the set of prime numbers less than 12. $E$ is the set of even numbers less than 12. $... show full transcript

Worked Solution & Example Answer:Represent these sets on the Venn diagram - Junior Cycle Mathematics - Question (a) - 2013

Step 1

Name any set on this diagram (after part (a) has been completed) that is a null set.

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Answer

The set $P \cap E$ is a null set since there are no numbers that are both prime and even, except for 2, which is not included in the intersection with odd.

Step 2

If a number is drawn at random from set P, what is the probability that it is even?

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Answer

Set $P = \{2, 3, 5, 7, 11\}$ contains 5 elements, and the only even number is 2. Thus, the probability is calculated as:

$P(even) = \frac{number\ of\ even\ elements\ in\ P}{total\ elements\ in\ P} = \frac{1}{5}.$

Therefore, the probability that a number drawn from set P is even is $\frac{1}{5}$ .

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