| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | One unknown from sum constraint only |
| Difficulty | Easy -1.3 This is a straightforward discrete probability distribution question requiring only basic probability axioms (probabilities sum to 1) and standard expectation/variance formulas. Part (i) is trivial arithmetic, part (ii) is routine calculation from definitions, and part (iii) applies basic independence. No problem-solving insight needed, just mechanical application of standard S1 techniques. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(r\) | 0 | 1 | 2 | 3 | 4 |
| \(\mathrm { P } ( X = r )\) | \(p\) | 0.1 | 0.05 | 0.05 | 0.25 |
4 A zoologist is studying the feeding behaviour of a group of 4 gorillas. The random variable $X$ represents the number of gorillas that are feeding at a randomly chosen moment. The probability distribution of $X$ is shown in the table below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$r$ & 0 & 1 & 2 & 3 & 4 \\
\hline
$\mathrm { P } ( X = r )$ & $p$ & 0.1 & 0.05 & 0.05 & 0.25 \\
\hline
\end{tabular}
\end{center}
(i) Find the value of $p$.\\
(ii) Find the expectation and variance of $X$.\\
(iii) The zoologist observes the gorillas on two further occasions. Find the probability that there are at least two gorillas feeding on both occasions.
\hfill \mbox{\textit{OCR MEI S1 Q4 [8]}}