A-LevelMathematicsProbability and statistics9709/51 · Oct/Nov 2025 · Q45 Marks

Bag A contains 8 red marbles and 3 blue marbles. Bag B contains 4 red marbles and 1 blue marble. A marble is chosen at random from bag A. If the marble chosen is red, it is discarded. If the marble chosen is blue, it is placed in bag B. A marble is then chosen at random from bag B. If the marble chosen is red, it is discarded. If the marble chosen is blue, it is placed in bag A. A marble is now chosen at random from bag A. (a) Complete the tree diagram below by entering all the remaining outcomes and probabilities. [3] [Tree diagram with some branches and probabilities: Bag A Red (8/11) Bag B (empty for now) Bag A (empty for now) Blue (3/11) Bag B Red (4/6) Bag A (empty for now) Blue (2/6) Bag A (empty for now) ]

(a)Complete the tree diagram below by entering all the remaining outcomes and probabilities.[3]
(b)Find the probability that all three marbles chosen are the same colour.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[B1] Bag B branches completed correctly including Red/Blue.
[B1] 2 sets of Bag A branches completely correctly including Red/Blue.
[B1] Final 2 sets of Bag A branches completely correctly including Red/Blue. Penalise omission of Red/Blue only once. If not identified, assume RB continues as for first Bag A.
[M1] Both, FT their tree diagram probabilities. May be seen in 4(a).
[A1] 0.4320661... to 3 or more SF.

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