CAIE FP2 2011 June — Question 7

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2011
SessionJune
TopicGeometric Distribution
TypeFind minimum n for P(X ≤ n) > threshold

7 A fair die is thrown until a 6 appears for the first time. Assuming that the throws are independent, find
  1. the probability that exactly 5 throws are needed,
  2. the probability that fewer than 8 throws are needed,
  3. the least integer \(n\) such that the probability of obtaining a 6 before the \(n\)th throw is at least 0.99 .