CAIE S1 2009 November — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2009
SessionNovember
TopicApproximating Binomial to Normal Distribution
TypeCombined binomial and normal events

6 A box contains 4 pears and 7 oranges. Three fruits are taken out at random and eaten. Find the probability that
  1. 2 pears and 1 orange are eaten, in any order,
  2. the third fruit eaten is an orange,
  3. the first fruit eaten was a pear, given that the third fruit eaten is an orange. There are 121 similar boxes in a warehouse. One fruit is taken at random from each box.
  4. Using a suitable approximation, find the probability that fewer than 39 are pears.