CAIE S1 2015 November — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2015
SessionNovember
TopicDiscrete Probability Distributions
TypeSum or difference of two spinners/dice

6 A fair spinner \(A\) has edges numbered \(1,2,3,3\). A fair spinner \(B\) has edges numbered \(- 3 , - 2 , - 1,1\). Each spinner is spun. The number on the edge that the spinner comes to rest on is noted. Let \(X\) be the sum of the numbers for the two spinners.
  1. Copy and complete the table showing the possible values of \(X\).
    Spinner \(A\)
    \cline { 2 - 6 }1233
    Spinner \(B\)- 2
    - 21
    - 1
    1
  2. Draw up a table showing the probability distribution of \(X\).
  3. Find \(\operatorname { Var } ( X )\).
  4. Find the probability that \(X\) is even, given that \(X\) is positive.