OCR S1 2009 January — Question 3

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2009
SessionJanuary
TopicGeometric Distribution
TypeMean/expectation of geometric distribution

3 Erika is a birdwatcher. The probability that she will see a woodpecker on any given day is \(\frac { 1 } { 8 }\). It is assumed that this probability is unaffected by whether she has seen a woodpecker on any other day.
  1. Calculate the probability that Erika first sees a woodpecker
    (a) on the third day,
    (b) after the third day.
  2. Find the expectation of the number of days up to and including the first day on which she sees a woodpecker.
  3. Calculate the probability that she sees a woodpecker on exactly 2 days in the first 15 days.