| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 3 |
| Topic | Discrete Probability Distributions |
| Type | Comparison or ordering of two independent values |
| Difficulty | Standard +0.3 This requires constructing a sample space of ordered pairs, identifying favorable outcomes where the second value exceeds the first, and calculating probabilities using independence. It's slightly above average difficulty due to the systematic enumeration needed, but the probability calculations themselves are straightforward multiplication and addition. |
| Spec | 2.03a Mutually exclusive and independent events |
| \(x\) | 1 | 2 | 3 |
| \(\mathrm { P } ( X = x )\) | 0.6 | 0.3 | 0.1 |
9 The probability distribution of a random variable $X$ is given in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
$x$ & 1 & 2 & 3 \\
\hline
$\mathrm { P } ( X = x )$ & 0.6 & 0.3 & 0.1 \\
\hline
\end{tabular}
\end{center}
Two values of $X$ are chosen at random.
Find the probability that the second value is greater than the first.
\hfill \mbox{\textit{OCR AS Pure 2017 Q9 [3]}}