| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | January |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Correct ordering probability |
| Difficulty | Easy -1.2 This is a straightforward probability question requiring basic counting principles. Part (i) is trivial (1/10000), and part (ii) requires recognizing there are 4! = 24 permutations of 4 distinct digits, giving probability 1/24. Both parts are routine applications of fundamental counting with no problem-solving insight needed. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(\text{Guess correctly}) = 0.1^4 = 0.0001\) | B1 CAO | [1] |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(\text{Guess correctly}) = \frac{1}{4!} = \frac{1}{24}\) | M1, A1 CAO | [2] |
| TOTAL | [3] |
## (i)
$P(\text{Guess correctly}) = 0.1^4 = 0.0001$ | B1 CAO | [1]
## (ii)
$P(\text{Guess correctly}) = \frac{1}{4!} = \frac{1}{24}$ | M1, A1 CAO | [2]
**TOTAL** | | [3]
---My credit card has a 4-digit code called a PIN. You should assume that any 4-digit number from 0000 to 9999 can be a PIN.
\begin{enumerate}[label=(\roman*)]
\item If I cannot remember any digits and guess my number, find the probability that I guess it correctly. [1]
\end{enumerate}
In fact my PIN consists of four different digits. I can remember all four digits, but cannot remember the correct order.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item If I now guess my number, find the probability that I guess it correctly. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2010 Q5 [3]}}