CAIE S1 2013 June — Question 7

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2013
SessionJune
TopicConditional Probability
TypeConditional probability with given score/outcome

7 Susan has a bag of sweets containing 7 chocolates and 5 toffees. Ahmad has a bag of sweets containing 3 chocolates, 4 toffees and 2 boiled sweets. A sweet is taken at random from Susan's bag and put in Ahmad's bag. A sweet is then taken at random from Ahmad's bag.
  1. Find the probability that the two sweets taken are a toffee from Susan's bag and a boiled sweet from Ahmad's bag.
  2. Given that the sweet taken from Ahmad's bag is a chocolate, find the probability that the sweet taken from Susan's bag was also a chocolate.
  3. The random variable \(X\) is the number of times a chocolate is taken. State the possible values of \(X\) and draw up a table to show the probability distribution of \(X\).