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Higher November 2022 Paper 2 Q14

EduqasHigherCurrent spec6 marksTree Diagrams

14. Dora has two boxes, \(A\) and \(B\).
The boxes contain beads which are identical in shape.

Box \(A\) contains 9 green, 6 red and 5 yellow beads.
Box \(B\) contains 12 red and 8 yellow beads.

Dora takes a bead at random from box \(A\). If the bead is:

  • green, she puts it back in box \(A\)
  • red or yellow, she puts it in box \(B\).

She then takes a bead at random from box \(B\).

(a) Complete the tree diagram. [3]
Tree diagram: Box A branches Green 9/20, Red 6/20, Yellow 5/20; each followed by Box B branches Red and Yellow with blank probabilities
(b) Find the probability that Dora takes two beads of the same colour. [3]