Sequential selection with conditional outcomes

Questions involving a sequence of selections where items are transferred between containers or where the order of selection matters for the probability calculation.

1 questions · Challenging +1.2

2.03a Mutually exclusive and independent events
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OCR H240/02 2018 September Q13
7 marks Challenging +1.2
13 Bag A contains 3 black discs and 2 white discs only. Initially Bag B is empty. Discs are removed at random from bag A, and are placed in bag B, one at a time, until all 5 discs are in bag B.
  1. Write down the probability that the last disc that is placed in bag B is black.
  2. Find the probability that the first disc and the last disc that are placed in bag B are both black.
  3. Find the probability that, starting from when the first disc is placed in bag B , the number of black discs in bag B is always greater than the number of white discs in bag B.