2026 PHS P2 Q5

2026 PHS P2 Q5

Secondary 4
8 marks
  1. \(\mathcal E=\{\text{integers}\hspace{0.5em}x:1\le x\le15\}\)
    \(A=\{\text{multiples of}\hspace{0.5em}2\}\)
    \(B=\{\text{factors of}\hspace{0.5em}24\}\)
    1. Explain why it is not true that \(B\subset A\).[1]
    2. List the elements of \(A\cup B\).[1]
  2. Set \(X\) and set \(Y\) are such that \(X\cap Y=\varnothing\).
    In the space below,
    1. complete the Venn diagram to represent set \(X\) and set \(Y\),
    2. shade the region on your diagram which represents \((X\cup Y)\prime\).[2]
  3. A bag contains 16 balls.
    9 of the balls are black and the rest are white.
    One ball is taken at random from the bag.
    If the ball is black, it is not put back into the bag.
    If the ball is white, it is put back into the bag.
    A second ball is then taken at random from the bag.
    Part of the tree diagram that represents these outcomes is drawn below.
    1. Complete the tree diagram.[2]
      \(\frac{9}{16}\)
      Black
      \(\frac{7}{16}\)
      White
      ______
      Black
      ______
      White
      ______
      Black
      ______
      White
      First ball
      Second ball
    2. Find, as a fraction in its simplest form, the probability that the two balls are of different colours.[2]

Solution:

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Answer:(a)(i) \(1\in B\) but \(1\notin A\). (ii) \(\{1,2,3,4,6,8,10,12,14\}\) (b) See Venn diagram. (c)(i) \(\dfrac8{15},\dfrac7{15},\dfrac9{16},\dfrac7{16}\) (ii) \(\dfrac{651}{1280}\)

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