| Exam Board | WJEC |
|---|---|
| Module | Unit 4 (Unit 4) |
| Year | 2019 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Sequential trials until success |
| Difficulty | Standard +0.3 This is a standard geometric probability question involving sequential trials. Part (a) requires straightforward probability calculations with given turn structures. Part (b) involves summing an infinite geometric series, which is a routine A-level technique. The question is slightly easier than average because the setup is clear, the methods are standard (geometric distribution/series), and part (b) is scaffolded as a 'show that' question. |
| Spec | 5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1) |
Four children are playing a game in order to win a calculator. They take turns, starting with Alex, followed by Ben, then Caroline, then Danielle, rolling a fair six-sided dice until someone obtains a 6. This player then wins a calculator.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that
\begin{enumerate}[label=(\roman*)]
\item Danielle wins the calculator on her first turn, [1]
\item Ben wins the calculator on his first or second turn, [3]
\item Caroline rolls the dice exactly twice. [3]
\end{enumerate}
\item Show that the probability that Alex wins the calculator is $\frac{216}{671}$. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 4 2019 Q2 [10]}}