CAIE FP2 2017 November — Question 6

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2017
SessionNovember
TopicGeometric Distribution
TypeCompound event with two dice/coins

6 A pair of fair dice is thrown repeatedly until a pair of sixes is obtained. The number of throws taken is denoted by the random variable \(X\).
  1. Find the mean value of \(X\).
  2. Find the probability that exactly 12 throws are required to obtain a pair of sixes.
  3. Find the probability that more than 12 throws are required to obtain a pair of sixes.