| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Conditional probability with random variables |
| Difficulty | Standard +0.8 This question requires understanding of discrete probability distributions and conditional probability. Part (a) is straightforward calculation, but part (b) requires careful application of conditional probability P(A|B) = P(A∩B)/P(B), involving summing specific terms from the distribution where x is both even AND less than 10, then dividing by the sum over all even values. The algebraic manipulation of sums and the two-step conditional probability reasoning elevate this above routine exercises. |
| Spec | 2.04a Discrete probability distributions |
14 A random variable $X$ has probability distribution given by $\mathrm { P } ( X = x ) = \frac { 1 } { 860 } ( 1 + x )$ for $x = 1,2,3 , \ldots , 40$.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { P } ( X > 39 )$.
\item Given that $x$ is even, determine $\mathrm { P } ( X < 10 )$.
\section*{END OF QUESTION PAPER}
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 Q14 [8]}}