CAIE S1 2014 November — Question 7

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2014
SessionNovember
TopicConditional Probability
TypeProbability distribution from conditional setup

7 A box contains 2 green apples and 2 red apples. Apples are taken from the box, one at a time, without replacement. When both red apples have been taken, the process stops. The random variable \(X\) is the number of apples which have been taken when the process stops.
  1. Show that \(\mathrm { P } ( X = 3 ) = \frac { 1 } { 3 }\).
  2. Draw up the probability distribution table for \(X\). Another box contains 2 yellow peppers and 5 orange peppers. Three peppers are taken at random from the box without replacement.
  3. Given that at least 2 of the peppers taken from the box are orange, find the probability that all 3 peppers are orange.