| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Direct binomial probability calculation |
| Difficulty | Moderate -0.3 This is a straightforward S1 binomial probability question requiring standard calculations with given parameters (n=50, p=0.08 and n=15, p=0.025). Parts (a) and (b) involve direct application of binomial probability formulas or tables with complementary probability. Part (c) requires combining results but the logic is clearly signposted. Slightly easier than average due to clear structure and routine calculations, though the multi-part nature and final probability reasoning prevent it from being trivial. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | 6 | 6" |
I appreciate you sharing this content, but I'm unable to clean it up as the material you've provided appears incomplete or unclear. The text shows:
"Question 7:
7 | 6 | 6"
This doesn't contain:
- Marking annotations (M1, A1, B1, etc.)
- Mathematical symbols to convert to LaTeX
- Guidance notes
- Clear marking points to format
Could you please provide the full mark scheme content for Question 7? It should include the actual marking criteria, solution steps, and point allocations.7 A travel agency in Tunisia offers customers a 3-day tour into the Sahara desert by either coach or minibus.
\begin{enumerate}[label=(\alph*)]
\item The agency accepts bookings from 50 customers for seats on the coach. The probability that a customer, who has booked a seat on the coach, will not turn up to claim the seat is 0.08 , and may be assumed to be independent of the behaviour of other customers.
Determine the probability that, of the customers who have booked a seat on the coach:
\begin{enumerate}[label=(\roman*)]
\item two or more will not turn up;
\item three or more will not turn up.
\end{enumerate}\item The agency accepts bookings from 15 customers for seats on the minibus. The probability that a customer, who has booked a seat on the minibus, will not turn up to claim the seat is 0.025 , and may be assumed to be independent of the behaviour of other customers.
Calculate the probability that, of the customers who have booked a seat on the minibus:
\begin{enumerate}[label=(\roman*)]
\item all will turn up;
\item one or more will not turn up.
\end{enumerate}\item The coach has 48 seats and the minibus has 14 seats. If 14 or fewer customers who have booked seats on the minibus turn up, they will be allocated a seat on the minibus. If all 15 customers who have booked seats on the minibus turn up, one will be allocated a seat on the coach. This will leave only 47 seats available for the 50 customers who have booked seats on the coach.
Use your results from parts (a) and (b) to calculate the probability that there will be seats available on the coach for all those who turn up having booked such seats.\\
(4 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2008 Q7 [12]}}