| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | One unknown from sum constraint only |
| Difficulty | Moderate -0.3 Part (i) is a straightforward application of the fact that probabilities sum to 1, requiring simple algebra to solve for p. Part (ii) requires understanding that the product is 0 when at least one value is 0, involving probability of sampling with/without replacement (likely with replacement given the context), but this is a standard probability calculation. The question tests basic probability concepts without requiring novel insight or complex multi-step reasoning. |
| Spec | 2.03a Mutually exclusive and independent events2.04a Discrete probability distributions |
| \(x\) | 0 | 2 | 4 | 6 |
| P\((X = x)\) | \(\frac{3}{8}\) | \(\frac{5}{16}\) | \(4p\) | \(p\) |
The probability distribution of a random variable $X$ is given in the table.
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 2 & 4 & 6 \\
\hline
P$(X = x)$ & $\frac{3}{8}$ & $\frac{5}{16}$ & $4p$ & $p$ \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\roman*)]
\item Find the value of $p$. [2]
\item Two values of $X$ are chosen at random. Find the probability that the product of these values is 0. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q10 [5]}}