CAIE S1 2020 March — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2020
SessionMarch
TopicTree Diagrams
TypeTwo-stage sampling with replacement

6 Box \(A\) contains 7 red balls and 1 blue ball. Box \(B\) contains 9 red balls and 5 blue balls. A ball is chosen at random from box \(A\) and placed in box \(B\). A ball is then chosen at random from box \(B\). The tree diagram below shows the possibilities for the colours of the balls chosen.
  1. Complete the tree diagram to show the probabilities. Box \(A\)
    \includegraphics[max width=\textwidth, alt={}, center]{f7c0e35d-1889-4e5b-b094-f467052a66cf-08_624_428_667_621} \section*{Box \(B\)} Red Blue Red Blue
  2. Find the probability that the two balls chosen are not the same colour.
  3. Find the probability that the ball chosen from box \(A\) is blue given that the ball chosen from box \(B\) is blue.