| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Basic probability calculation |
| Difficulty | Easy -1.2 This is a straightforward S1 probability question testing basic set operations (complement, intersection, union), independence across trials, and the law of total probability. All parts require direct application of standard formulas with no problem-solving insight needed—purely routine calculations that any well-prepared S1 student should handle mechanically. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| I appreciate you sharing this content, but I'm unable to process it as presented. The text "Question 5: 5 | 24 | 30" doesn't contain mark scheme content with marking annotations (M1, A1, B1, etc.) or unicode symbols to convert. |
I appreciate you sharing this content, but I'm unable to process it as presented. The text "Question 5: 5 | 24 | 30" doesn't contain mark scheme content with marking annotations (M1, A1, B1, etc.) or unicode symbols to convert.
Could you please provide the full mark scheme content for Question 5? It should include elements like:
- Method marks (M1, M2, etc.)
- Accuracy marks (A1, A2, etc.)
- Marking annotations and guidance notes
- Mathematical notation that needs cleaning
Once you share the complete content, I'll be happy to convert it to the format you've requested.5 A health club has a number of facilities which include a gym and a sauna. Andrew and his wife, Heidi, visit the health club together on Tuesday evenings.
On any visit, Andrew uses either the gym or the sauna or both, but no other facilities. The probability that he uses the gym, $\mathrm { P } ( G )$, is 0.70 . The probability that he uses the sauna, $\mathrm { P } ( S )$, is 0.55 . The probability that he uses both the gym and the sauna is 0.25 .
\begin{enumerate}[label=(\alph*)]
\item Calculate the probability that, on a particular visit:
\begin{enumerate}[label=(\roman*)]
\item he does not use the gym;
\item he uses the gym but not the sauna;
\item he uses either the gym or the sauna but not both.
\end{enumerate}\item Assuming that Andrew's decision on what facility to use is independent from visit to visit, calculate the probability that, during a month in which there are exactly four Tuesdays, he does not use the gym.
\item The probability that Heidi uses the gym when Andrew uses the gym is 0.6 , but is only 0.1 when he does not use the gym.
Calculate the probability that, on a particular visit, Heidi uses the gym.
\item On any visit, Heidi uses exactly one of the club's facilities.
The probability that she uses the sauna is 0.35 .\\
Calculate the probability that, on a particular visit, she uses a facility other than the gym or the sauna.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2008 Q5 [12]}}