| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Population partition tree diagram |
| Difficulty | Easy -1.2 This is a straightforward application of tree diagrams and basic probability rules. Part (a) requires drawing a standard two-stage tree diagram with given probabilities. Part (b) uses the law of total probability (a routine AS-level technique). Part (c) applies the independence assumption with a simple power calculation. All steps are mechanical with no problem-solving insight required, making this easier than average. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.2 \times 0.4\) or \(0.8 \times 0.9\) | M1 | Ft (a) |
| \(0.2 \times 0.4 + 0.8 \times 0.9\) | A1 | Ft (a) |
| \(0.8\) cao | A1 | Accept \(\frac{4}{5}\) or 80%; working may be on diagram in (a) |
| Answer | Marks | Guidance |
|---|---|---|
| \((\text{their } 0.8)^5\) | M1 | |
| \(0.328\) or \(0.3277\) or \(0.32768\) | A1 | \(\frac{1024}{3125}\); accept \(0.33\); accept as percentage |
# Question 5:
## Part (b):
$0.2 \times 0.4$ or $0.8 \times 0.9$ | M1 | Ft (a)
$0.2 \times 0.4 + 0.8 \times 0.9$ | A1 | Ft (a)
$0.8$ cao | A1 | Accept $\frac{4}{5}$ or 80%; working may be on diagram in (a)
## Part (c):
$(\text{their } 0.8)^5$ | M1 |
$0.328$ or $0.3277$ or $0.32768$ | A1 | $\frac{1024}{3125}$; accept $0.33$; accept as percentage
---5 Each day John either cycles to work or goes on the bus.
\begin{itemize}
\item If it is raining when John is ready to set off for work, the probability that he cycles to work is 0.4.
\item If it is not raining when John is ready to set off for work, the probability that he cycles to work is 0.9 .
\item The probability that it is raining when he is ready to set off for work is 0.2 .
\end{itemize}
You should assume that days on which it rains occur randomly and independently.
\begin{enumerate}[label=(\alph*)]
\item Draw a tree diagram to show the possible outcomes and their associated probabilities.
\item Calculate the probability that, on a randomly chosen day, John cycles to work. John works 5 days each week.
\item Calculate the probability that he cycles to work every day in a randomly chosen working week.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2019 Q5 [8]}}