| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Independent binomial samples with compound probability |
| Difficulty | Moderate -0.3 This is a straightforward binomial distribution question requiring standard recall and application. Part (i) asks for a condition (independence or constant probability), part (ii) is a direct binomial probability calculation, and part (iii) involves applying binomial distribution twice in succession. While part (iii) requires careful setup with nested binomial distributions, it follows a standard pattern with no novel problem-solving required. The question is slightly easier than average due to its routine nature and clear structure. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
The probability that Janice sees a kingfisher on any particular day is 0.3. She notes the number, $X$, of days in a week on which she sees a kingfisher.
\begin{enumerate}[label=(\roman*)]
\item State one necessary condition for $X$ to have a binomial distribution. [1]
\end{enumerate}
Assume now that $X$ has a binomial distribution.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the probability that, in a week, Janice sees a kingfisher on exactly 2 days. [1]
\end{enumerate}
Each week Janice notes the number of days on which she sees a kingfisher.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Find the probability that Janice sees a kingfisher on exactly 2 days in a week during at least 4 of 6 randomly chosen weeks. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q11 [5]}}