OCR H240/02 2020 November — Question 13 8 marks

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Year2020
SessionNovember
Marks8
PaperDownload PDF ↗
TopicProbability Definitions
TypeSequential events and tree diagrams
DifficultyStandard +0.8 This question requires careful enumeration of outcomes in an unusual game structure, then extends to an infinite geometric series for the match probability. Part (a) demands systematic case analysis of 3-point sequences, while part (b) requires recognizing and summing a geometric series involving conditional probabilities—going beyond routine probability tree exercises to require genuine problem-solving insight.
Spec2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space

Andy and Bev are playing a game.
  • The game consists of three points.
  • On each point, P(Andy wins) = 0.4 and P(Bev wins) = 0.6.
  • If one player wins two consecutive points, then they win the game, otherwise neither player wins.
  1. Determine the probability of the following events.
    1. Andy wins the game. [2]
    2. Neither player wins the game. [3]
Andy and Bev now decide to play a match which consists of a series of games.
  • In each game, if a player wins the game then they win the match.
  • If neither player wins the game then the players play another game.
  1. Determine the probability that Andy wins the match. [3]

Andy and Bev are playing a game.
\begin{itemize}
\item The game consists of three points.
\item On each point, P(Andy wins) = 0.4 and P(Bev wins) = 0.6.
\item If one player wins two consecutive points, then they win the game, otherwise neither player wins.
\end{itemize}

\begin{enumerate}[label=(\alph*)]
\item Determine the probability of the following events.
\begin{enumerate}[label=(\roman*)]
\item Andy wins the game. [2]
\item Neither player wins the game. [3]
\end{enumerate}
\end{enumerate}

Andy and Bev now decide to play a match which consists of a series of games.
\begin{itemize}
\item In each game, if a player wins the game then they win the match.
\item If neither player wins the game then the players play another game.
\end{itemize}

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the probability that Andy wins the match. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/02 2020 Q13 [8]}}