| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Venn diagram with two events |
| Difficulty | Moderate -0.8 This is a straightforward Venn diagram problem requiring basic set operations and conditional probability. Students need to organize given information (total 120, dogs 57, both 16, neither 35), calculate missing values, then apply simple probability formulas including P(A|B). The calculations are routine with no conceptual challenges beyond standard S1 material. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\frac{57-16}{120} = \frac{41}{120}\) | M1 A1 | |
| (b) \(\frac{85}{120} = P(C) + \frac{57}{120} - \frac{16}{120}\) | M2 | |
| \(P(C) = \frac{85-57+16}{120} = \frac{44}{120} = \frac{11}{30}\) | M1 A1 | |
| (c) \(P(C' | D') = \frac{P(C' \cap D')}{P(D')}\) | M2 |
| \(= \frac{\frac{35}{120}}{1 - \frac{57}{120}} = \frac{35}{63} = \frac{5}{9}\) | M1 A1 | (10 marks total) |
(a) $\frac{57-16}{120} = \frac{41}{120}$ | M1 A1 |
(b) $\frac{85}{120} = P(C) + \frac{57}{120} - \frac{16}{120}$ | M2 |
$P(C) = \frac{85-57+16}{120} = \frac{44}{120} = \frac{11}{30}$ | M1 A1 |
(c) $P(C'|D') = \frac{P(C' \cap D')}{P(D')}$ | M2 |
$= \frac{\frac{35}{120}}{1 - \frac{57}{120}} = \frac{35}{63} = \frac{5}{9}$ | M1 A1 | (10 marks total)3. In a study of 120 pet-owners it was found that 57 owned at least one dog and of these 16 also owned at least one cat. There were 35 people in the group who didn't own any cats or dogs.
As an incentive to take part in the study, one participant is chosen at random to win a year's free supply of pet food.
Find the probability that the winner of this prize
\begin{enumerate}[label=(\alph*)]
\item owns a dog but does not own a cat,
\item owns a cat,
\item does not own a cat given that they do not own a dog.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [10]}}