| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Probability distribution from formula |
| Difficulty | Challenging +1.2 Part (a) is routine substitution into a given formula. Part (b) requires systematic enumeration of cases where X₃ > X₁ + X₂, calculating probabilities for each outcome combination - this involves careful organization and multiple probability calculations but uses standard techniques without requiring novel insight. The computational demand and case-work elevate it slightly above average difficulty. |
| Spec | 2.04a Discrete probability distributions |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{2}{5} \quad \frac{3}{10} \quad \frac{1}{5} \quad \frac{1}{10}\) oe | B1 (1.1) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\left(\frac{2}{5}\right)^2\times\frac{1}{5} + \left(\frac{2}{5}\right)^2\times\frac{1}{10} + \frac{2}{5}\times\frac{3}{10}\times\frac{1}{10} + \frac{3}{10}\times\frac{2}{5}\times\frac{1}{10}\) | B1 (3.1a) | B1 for any three of these soi, e.g. on tree diagram |
| M1 (2.1) | Any two correct products added: ft their table | |
| \(= \frac{9}{125}\) or \(0.072\) | A1 (1.1) |
# Question 11(a):
$1 \quad 2 \quad 3 \quad 4$
$\frac{2}{5} \quad \frac{3}{10} \quad \frac{1}{5} \quad \frac{1}{10}$ oe | B1 (1.1) | B1
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# Question 11(b):
DR: $1,1,3$; $1,1,4$; $1,2,4$; $2,1,4$
$\left(\frac{2}{5}\right)^2\times\frac{1}{5} + \left(\frac{2}{5}\right)^2\times\frac{1}{10} + \frac{2}{5}\times\frac{3}{10}\times\frac{1}{10} + \frac{3}{10}\times\frac{2}{5}\times\frac{1}{10}$ | B1 (3.1a) | B1 for any three of these soi, e.g. on tree diagram
| M1 (2.1) | Any two correct products added: ft their table
$= \frac{9}{125}$ or $0.072$ | A1 (1.1) |11 In this question you must show detailed reasoning.
A biased four-sided spinner has edges numbered $1,2,3,4$. When the spinner is spun, the probability that it will land on the edge numbered $X$ is given by\\
$P ( X = x ) = \begin{cases} \frac { 1 } { 2 } - \frac { 1 } { 10 } x & x = 1,2,3,4 , \\ 0 & \text { otherwise } . \end{cases}$
\begin{enumerate}[label=(\alph*)]
\item Draw a table showing the probability distribution of $X$.
The spinner is spun three times and the value of $X$ is noted each time.
\item Find the probability that the third value of $X$ is greater than the sum of the first two values of $X$.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q11 [4]}}