2025 IGCSE 0580 October/November P21 Q20

2025 IGCSE 0580 October/November P21 Q20

9 marks

Bag A contains 5 white balls and 3 black balls.

Bag B contains 3 white balls and 1 black ball.

  1. Two balls are picked at random from bag B without replacement.
    Find the probability that both balls are black.[1]
  2. The balls are replaced into bag B.
    Kyle picks a ball at random from each bag.
    1. Complete the tree diagram.[2]
      \(\dfrac{5}{8}\)
      white
      ........
      black
      ........
      white
      ........
      black
      ........
      white
      ........
      black
      Bag A
      Bag B
    2. Find the probability that the two balls are the same colour.[3]
  3. The balls are replaced into their bags.
    Jo picks a ball at random from bag A and places it into bag B.
    She then picks a ball at random from bag B.
    Find the probability that she picks a black ball from bag B.[3]

Solution:

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Answer:(a) \(0\). (b)(i) Bag A: \(\dfrac38\); each Bag B split: \(\dfrac34,\dfrac14\). (ii) \(\dfrac9{16}\). (c) \(\dfrac{11}{40}\).

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