OCR S1 2014 June — Question 9

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2014
SessionJune
TopicGeometric Distribution
TypeP(a ≤ X ≤ b) range probability

9 Each day Harry makes repeated attempts to light his gas fire. If the fire lights he makes no more attempts. On each attempt, the probability that the fire will light is 0.3 independent of all other attempts. Find the probability that
  1. the fire lights on the 5th attempt,
  2. Harry needs more than 1 attempt but fewer than 5 attempts to light the fire. If the fire does not light on the 6th attempt, Harry stops and the fire remains unlit.
  3. Find the probability that, on a particular day, the fire lights.
  4. Harry's week starts on Monday. Find the probability that, during a certain week, the first day on which the fire lights is Wednesday.