| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Sum or difference of two spinners/dice |
| Difficulty | Moderate -0.8 This is a straightforward S1 probability distribution question involving basic counting of outcomes (choosing 2 from 4 cards with one repeated value), calculating probabilities, and applying standard formulas for expectation and variance. The enumeration is simple with only 6 possible pairs, and all required techniques are routine applications of definitions with no problem-solving insight needed. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| 1 | 2 | 3 | 3 |
Each of four cards has a number printed on it as shown.
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
1 & 2 & 3 & 3 \\
\hline
\end{tabular}
\end{center}
Two of the cards are chosen at random, without replacement. The random variable $X$ denotes the sum of the numbers on these two cards.
\begin{enumerate}[label=(\roman*)]
\item Show that P$(X = 6) = \frac{1}{6}$ and P$(X = 4) = \frac{1}{3}$. [3]
\item Write down all the possible values of $X$ and find the probability distribution of $X$. [4]
\item Find E$(X)$ and Var$(X)$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2010 Q5 [12]}}