| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Geometric Distribution |
| Type | P(a ≤ X ≤ b) range probability |
| Difficulty | Standard +0.3 This is a straightforward geometric distribution question with standard applications. Part (i) requires recognizing the geometric distribution and basic probability calculations, part (ii) uses the standard expectation formula E(X)=1/p, and part (iii) applies conditional probability with simple counting. All techniques are routine for Further Statistics students with no novel insight required. |
| Spec | 5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)5.02h Geometric: mean 1/p and variance (1-p)/p^2 |
A bag contains 3 green counters, 3 blue counters and $w$ white counters. Counters are selected at random, one at a time, with replacement, until a white counter is drawn. The total number of counters selected, including the white counter, is denoted by $X$.
\begin{enumerate}[label=(\roman*)]
\item In the case when $w = 2$,
\begin{enumerate}[label=(\alph*)]
\item write down the distribution of $X$, [1]
\item find $P(3 < X \leq 7)$. [2]
\end{enumerate}
\item In the case when E$(X) = 2$, determine the value of $w$. [2]
\item In the case when $w = 2$ and $X = 6$, find the probability that the first five counters drawn alternate in colour. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2017 Q6 [7]}}