AQA S1 2011 June — Question 5

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2011
SessionJune
TopicProbability Definitions
TypeVenn diagram completion
5
  1. Emma visits her local supermarket every Thursday to do her weekly shopping. The event that she buys orange juice is denoted by \(J\), and the event that she buys bottled water is denoted by \(W\). At each visit, Emma may buy neither, or one, or both of these items.
    1. Complete the table of probabilities, printed below, for these events, where \(J ^ { \prime }\) and \(W ^ { \prime }\) denote the events 'not \(J\) ' and 'not \(W ^ { \prime }\) respectively.
    2. Hence, or otherwise, find the probability that, on any given Thursday, Emma buys either orange juice or bottled water but not both.
    3. Show that:
      (A) the events \(J\) and \(W\) are not mutually exclusive;
      (B) the events \(J\) and \(W\) are not independent.
  2. Rhys visits the supermarket every Saturday to do his weekly shopping. Items that he may buy are milk, cheese and yogurt. The probability, \(\mathrm { P } ( M )\), that he buys milk on any given Saturday is 0.85 .
    The probability, \(\mathrm { P } ( C )\), that he buys cheese on any given Saturday is 0.60 .
    The probability, \(\mathrm { P } ( Y )\), that he buys yogurt on any given Saturday is 0.55 .
    The events \(M , C\) and \(Y\) may be assumed to be independent. Calculate the probability that, on any given Saturday, Rhys buys:
    1. none of the 3 items;
    2. exactly 2 of the 3 items.
      \cline { 2 - 4 } \multicolumn{1}{c|}{}\(\boldsymbol { J }\)\(\boldsymbol { J } ^ { \prime }\)Total
      \(\boldsymbol { W }\)0.65
      \(\boldsymbol { W } ^ { \prime }\)0.15
      Total0.301.00
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