2025 CCHY PRELIMS P1 Q13

\(\xi=\{1,2,3,4,8,15,27,43,49,121\}\) \(L=\{\text{Prime Numbers}\hspace{0.15em}\}\) \(M=\{\text{Odd Numbers}\hspace{0.15em}\}\) \(N=\{\text{Square Numbers}\hspace{0.15em}\}\)

1. Complete the Venn diagram to illustrate this information. There are no elements in the shaded portion of the diagram.[2]
2. List the elements in \((M\cup L)'\).[1]
3. Find the value of \(n\big((L'\cup N)\cap(L\cup N')\big)\).[1]
4. The numbers in \(\xi\) are each printed on one card. If a card is picked at random from the ten cards, find the probability that the number printed on the card
   1. is a perfect cube,[1]
   2. is a multiple of 3.[1]