Mathematics 9709 · AS & A Level · Probability

Probability — practice question

Bag A holds 8 red marbles and 3 blue marbles. Bag B holds 4 red marbles and 1 blue marble. A marble is picked at random from bag A. If the marble picked is red, it is thrown away. If the marble picked is blue, it is put into bag B. A marble is then picked at random from bag B. If the marble picked is red, it is thrown away. If the marble picked is blue, it is put into bag A. A marble is now picked at random from bag A.
(a)[3]

Complete the tree diagram below by filling in every missing outcome and probability.

(b)[2]

Find the probability that all three marbles chosen are the same colour.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Bag B branches are completed accurately, including the Red/Blue labels

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