| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Sequential events and tree diagrams |
| Difficulty | Standard +0.3 This is a straightforward tree diagram problem with clearly stated probabilities and standard conditional probability calculations. Part (c) requires Bayes' theorem but in a routine context. All parts follow standard S1 techniques with no novel insight required, making it slightly easier than average. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(0.45 \times 0.6 = 0.27\) | M1 A1 | |
| (b) \(1 - (0.45 \times 0.4 \times 0.6) = 1 - 0.108 = 0.892\) | M2 A1 | |
| (c) \(P(\text{passed 1st time | passed}) = \frac{P(\text{passed 1st time} \cap \text{passed})}{P(\text{passed})} = \frac{0.55}{0.892} = 0.617\) (3sf) | M2 A1 |
| (d) 200 1st time, 120 2nd time, 80 3rd time; no. expected to pass \(= (200 \times 0.55) + (120 \times 0.6) + (80 \times 0.4) = 110 + 72 + 32 = 214\) | A1 M2 A1 | Total 12 marks |
**(a)** $0.45 \times 0.6 = 0.27$ | M1 A1 |
**(b)** $1 - (0.45 \times 0.4 \times 0.6) = 1 - 0.108 = 0.892$ | M2 A1 |
**(c)** $P(\text{passed 1st time | passed}) = \frac{P(\text{passed 1st time} \cap \text{passed})}{P(\text{passed})} = \frac{0.55}{0.892} = 0.617$ (3sf) | M2 A1 |
**(d)** 200 1st time, 120 2nd time, 80 3rd time; no. expected to pass $= (200 \times 0.55) + (120 \times 0.6) + (80 \times 0.4) = 110 + 72 + 32 = 214$ | A1 M2 A1 | Total 12 marks
---6. A software company sets exams for programmers who wish to qualify to use their packages. Past records show that $55 \%$ of candidates taking the exam for the first time will pass, $60 \%$ of those taking it for the second time will pass, but only $40 \%$ of those taking the exam for the third time will pass. Candidates are not allowed to sit the exam more than three times.
A programmer decides to keep taking the exam until he passes or is allowed no further attempts. Find the probability that he will
\begin{enumerate}[label=(\alph*)]
\item pass the exam on his second attempt,
\item pass the exam.
Another programmer already has the qualification.
\item Find, correct to 3 significant figures, the probability that she passed first time.
At a particular sitting of the exam there are 400 candidates.\\
The ratio of those sitting the exam for the first time to those sitting it for the second time to those sitting it for the third time is $5 : 3 : 2$
\item How many of the 400 candidates would be expected to pass?
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q6 [12]}}