| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Venn diagram completion |
| Difficulty | Easy -1.2 This is a straightforward Venn diagram probability question requiring basic addition of probabilities and checking independence using P(A∩T) = P(A)×P(T). All values are given or easily calculated with simple arithmetic; no problem-solving insight needed, just routine application of definitions. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
| Answer | Marks | Guidance |
|---|---|---|
| \(p = [1 - 0.75 - 0.05 =]\ \mathbf{0.20}\) | B1 | cao for \(p = 0.20\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(q = \mathbf{0.15}\) | B1ft | Ft for use of their \(p\) and \(P(A \text{ or } T)\) to find \(q\), i.e. \(0.75 -\) "\(p\)" \(- 0.40\) or \(q = 0.15\) |
| \(P(A) = 0.35,\ P(T) = 0.6,\ P(A \text{ and } T) = 0.20\); \(P(A) \times P(T) = 0.21\) | M1 | For the statement of all probabilities required for a suitable test and sight of any appropriate calculations required |
| Since \(0.20 \neq 0.21\) therefore \(A\) and \(T\) are not independent | A1 | All probabilities correct, correct comparison and suitable comment |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(\text{not } [A \text{ or } C]) = \mathbf{0.45}\) | B1 | cao for \(0.45\) |
## Question 3:
### Part (a):
$p = [1 - 0.75 - 0.05 =]\ \mathbf{0.20}$ | B1 | cao for $p = 0.20$
### Part (b):
$q = \mathbf{0.15}$ | B1ft | Ft for use of their $p$ and $P(A \text{ or } T)$ to find $q$, i.e. $0.75 -$ "$p$" $- 0.40$ **or** $q = 0.15$
$P(A) = 0.35,\ P(T) = 0.6,\ P(A \text{ and } T) = 0.20$; $P(A) \times P(T) = 0.21$ | M1 | For the statement of all probabilities required for a suitable test and sight of any appropriate calculations required
Since $0.20 \neq 0.21$ therefore $A$ and $T$ are **not** independent | A1 | All probabilities correct, correct comparison and suitable comment
### Part (c):
$P(\text{not } [A \text{ or } C]) = \mathbf{0.45}$ | B1 | cao for $0.45$
---\begin{enumerate}
\item The Venn diagram shows the probabilities for students at a college taking part in various sports.\\
$A$ represents the event that a student takes part in Athletics.\\
$T$ represents the event that a student takes part in Tennis.\\
$C$ represents the event that a student takes part in Cricket.\\
$p$ and $q$ are probabilities.\\
\includegraphics[max width=\textwidth, alt={}, center]{8f3dbcb4-3260-4493-a230-12577b4ed691-06_668_935_596_566}
\end{enumerate}
The probability that a student selected at random takes part in Athletics or Tennis is 0.75\\
(a) Find the value of $p$.\\
(b) State, giving a reason, whether or not the events $A$ and $T$ are statistically independent. Show your working clearly.\\
(c) Find the probability that a student selected at random does not take part in Athletics or Cricket.
\hfill \mbox{\textit{Edexcel AS Paper 2 Q3 [5]}}