OCR MEI Further Statistics Minor 2023 June — Question 1

Exam BoardOCR MEI
ModuleFurther Statistics Minor (Further Statistics Minor)
Year2023
SessionJune
TopicGeometric Distribution
TypeFirst success on specific trial

1 A fair spinner has ten sectors, labelled \(1,2 , \ldots , 10\). In order to start a game, Kofi has to obtain an 8,9 or 10 on the spinner.
  1. Find the probability that Kofi starts the game on the third spin.
  2. Find the probability that Kofi takes at least 5 spins to start the game.
  3. Determine the probability that the number of spins required to start the game is within 1 standard deviation of its mean.