CAIE S1 2020 November — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2020
SessionNovember
TopicDiscrete Probability Distributions
TypeConstruct probability distribution from scenario

4 The random variable \(X\) takes each of the values \(1,2,3,4\) with probability \(\frac { 1 } { 4 }\). Two independent values of \(X\) are chosen at random. If the two values of \(X\) are the same, the random variable \(Y\) takes that value. Otherwise, the value of \(Y\) is the larger value of \(X\) minus the smaller value of \(X\).
  1. Draw up the probability distribution table for \(Y\).
  2. Find the probability that \(Y = 2\) given that \(Y\) is even.