| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2020 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Sequential events and tree diagrams |
| Difficulty | Standard +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. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
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]}}