AQA S1 2015 June — Question 4

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2015
SessionJune
TopicTree Diagrams
TypeTwo independent categorical choices
4
  1. Chris shops at his local store on his way to and from work every Friday.
    The event that he buys a morning newspaper is denoted by \(M\), and the event that he buys an evening newspaper is denoted by \(E\). On any one Friday, Chris may buy neither, exactly one or both of these newspapers.
    1. Complete the table of probabilities, printed on the opposite page, where \(M ^ { \prime }\) and \(E ^ { \prime }\) denote the events 'not \(M\) ' and 'not \(E\) ' respectively.
    2. Hence, or otherwise, find the probability that, on any given Friday, Chris buys exactly one newspaper.
    3. Give a numerical justification for the following statement.
      'The events \(M\) and \(E\) are not mutually exclusive.'
  2. The event that Chris buys a morning newspaper on Saturday is denoted by \(S\), and the event that he buys a morning newspaper on the following day, Sunday, is denoted by \(T\). The event that he buys a morning newspaper on both Saturday and Sunday is denoted by \(S \cap T\). Each combination of the events \(S\) and \(T\) is independent of any combination of the events \(M\) and \(E\). However, the events \(S\) and \(T\) are not independent, with $$\mathrm { P } ( S ) = 0.85 , \quad \mathrm { P } ( T \mid S ) = 0.20 \quad \text { and } \quad \mathrm { P } \left( T \mid S ^ { \prime } \right) = 0.75$$ Find the probability that, on a particular Friday, Saturday and Sunday, Chris buys:
    1. all four newspapers;
    2. none of the four newspapers.
    1. State, as briefly as possible, in the context of the question, the event that is denoted by \(M \cap E ^ { \prime } \cap S \cap T ^ { \prime }\).
    2. Calculate the value of \(\mathrm { P } \left( M \cap E ^ { \prime } \cap S \cap T ^ { \prime } \right)\). \section*{Answer space for question 4}
    1. \cline { 2 - 4 } \multicolumn{1}{c|}{}\(\boldsymbol { M }\)\(\boldsymbol { M } ^ { \prime }\)Total
      \(\boldsymbol { E }\)0.160.28
      \(\boldsymbol { E } ^ { \prime }\)
      Total0.601.00
      \includegraphics[max width=\textwidth, alt={}]{4c679380-894f-4d36-aec8-296b662058e2-11_2050_1707_687_153}
This paper (7 questions)
View full paper
Q1 6 Q2 4 Q3 2 Q4 Q5 1 Q6 3 Q7 2