OCR S1 2007 January — Question 6

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2007
SessionJanuary
TopicGeometric Distribution
TypeP(X ≤ n) or P(X < n)

6 A coin is biased so that the probability that it will show heads on any throw is \(\frac { 2 } { 3 }\). The coin is thrown repeatedly. The number of throws up to and including the first head is denoted by \(X\). Find
  1. \(\mathrm { P } ( X = 4 )\),
  2. \(\mathrm { P } ( X < 4 )\),
  3. \(\mathrm { E } ( X )\).