| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2003 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Independence test with P(A∩B) = P(A)×P(B) |
| Difficulty | Easy -1.2 This is a straightforward S1 conditional probability question requiring basic probability calculations from a two-way table (reading values, computing P(A∩B), P(A'), and P(A|B')) and a routine independence check using P(A∩B) = P(A)×P(B). All steps are standard textbook exercises with no problem-solving insight needed. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Claim | No claim | |
| Zippy | 35 | 15 |
| Nifty | 40 | 10 |
2. A car dealer offers purchasers a three year warranty on a new car. He sells two models, the Zippy and the Nifty. For the first 50 cars sold of each model the number of claims under the warranty is shown in the table below.
\begin{center}
\begin{tabular}{ | c | c | c | }
\hline
& Claim & No claim \\
\hline
Zippy & 35 & 15 \\
\hline
Nifty & 40 & 10 \\
\hline
\end{tabular}
\end{center}
One of the purchasers is chosen at random. Let $A$ be the event that no claim is made by the purchaser under the warranty and $B$ the event that the car purchased is a Nifty.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { P } ( A \cap B )$.
\item Find $\mathrm { P } \left( A ^ { \prime } \right)$.
Given that the purchaser chosen does not make a claim under the warranty,
\item find the probability that the car purchased is a Zippy.
\item Show that making a claim is not independent of the make of the car purchased.
Comment on this result.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2003 Q2 [9]}}