Basic Inclusion-Exclusion with Two Sets

A question is this type if and only if it involves finding probabilities or counts using the inclusion-exclusion principle for exactly two events or sets, typically given P(A), P(B), and one other piece of information.

2 questions

OCR MEI S1 2016 June Q5
5 Measurements of sunshine and rainfall are made each day at a particular weather station. For a randomly chosen day,
  • \(R\) is the event that at least 1 mm of rainfall is recorded,
  • \(S\) is the event that at least 1 hour of sunshine is recorded.
You are given that \(\mathrm { P } ( R ) = 0.28 , \mathrm { P } ( S ) = 0.87\) and \(\mathrm { P } ( R \cup S ) = 0.94\).
  1. Find \(\mathrm { P } ( R \cap S )\).
  2. Draw a Venn diagram showing the events \(R\) and \(S\), and fill in the probability corresponding to each of the four regions of your diagram.
  3. Find \(\mathrm { P } ( R \mid S )\) and state what this probability represents in this context.
Edexcel S1 2004 November Q5
5. The events \(A\) and \(B\) are such that \(\mathrm { P } ( A ) = \frac { 1 } { 2 } , \mathrm { P } ( B ) = \frac { 1 } { 3 }\) and \(\mathrm { P } ( A \cap B ) = \frac { 1 } { 4 }\).
  1. Using the space below, represent these probabilities in a Venn diagram. Hence, or otherwise, find
  2. \(\mathrm { P } ( A \cup B )\),
  3. \(\mathrm { P } \left( \begin{array} { l l } A & B ^ { \prime } \end{array} \right)\)