CAIE S1 2005 November — Question 2

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2005
SessionNovember
TopicConditional Probability
TypeBayes with sampling without replacement

2 Boxes of sweets contain toffees and chocolates. Box \(A\) contains 6 toffees and 4 chocolates, box \(B\) contains 5 toffees and 3 chocolates, and box \(C\) contains 3 toffees and 7 chocolates. One of the boxes is chosen at random and two sweets are taken out, one after the other, and eaten.
  1. Find the probability that they are both toffees.
  2. Given that they are both toffees, find the probability that they both came from box \(A\).