CAIE FP2 2014 June — Question 6

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2014
SessionJune
TopicGeometric Distribution
TypeCompound event with two dice/coins

6 A pair of coins is thrown repeatedly until a pair of heads is obtained. The number of throws taken is denoted by the random variable \(X\). State the expected value of \(X\). Find the probability that
  1. exactly 4 throws are required to obtain a pair of heads,
  2. fewer than 6 throws are required to obtain a pair of heads.