| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Basic two-way table probability |
| Difficulty | Easy -1.3 This is a straightforward S1 question testing basic probability concepts from a two-way table. Part (a) requires simple reading of values and basic probability rules (complement, union, conditional probability), while part (b) involves a standard permutation calculation with replacement. All techniques are routine with no problem-solving insight required. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables5.01a Permutations and combinations: evaluate probabilities |
| \multirow{2}{*}{} | Subject category | |||||
| Crime | Romance | Science fiction | Thriller | Total | ||
| \multirow{2}{*}{Type} | Hardback | 8 | 16 | 18 | 18 | 60 |
| Paperback | 16 | 40 | 14 | 30 | 100 | |
| Total | 24 | 56 | 32 | 48 | 160 | |
1 A large bookcase contains two types of book: hardback and paperback. The number of books of each type in each of four subject categories is shown in the table.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{\multirow{2}{*}{}} & \multicolumn{4}{|c|}{Subject category} & \\
\hline
& & Crime & Romance & Science fiction & Thriller & Total \\
\hline
\multirow{2}{*}{Type} & Hardback & 8 & 16 & 18 & 18 & 60 \\
\hline
& Paperback & 16 & 40 & 14 & 30 & 100 \\
\hline
& Total & 24 & 56 & 32 & 48 & 160 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item A book is selected at random from the bookcase. Calculate the probability that the book is:
\begin{enumerate}[label=(\roman*)]
\item a paperback;
\item not science fiction;
\item science fiction or a hardback;
\item a thriller, given that it is a paperback.
\end{enumerate}\item Three books are selected at random, without replacement, from the bookcase.
Calculate, to three decimal places, the probability that one is crime, one is romance and one is science fiction.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2009 Q1 [11]}}