| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2013 |
| Session | November |
| Marks | 5 |
| Topic | Conditional Probability |
| Type | Independence test with P(A∩B) = P(A)×P(B) |
| Difficulty | Moderate -0.8 This is a straightforward probability question testing basic concepts of independence and conditional probability. Part (i) requires checking if P(G ∩ T) = P(G)×P(T) using simple multiplication. Part (ii) applies the standard conditional probability formula P(T|G) = P(G ∩ T)/P(G) with given values. Both parts involve routine calculations with no problem-solving insight required, making this easier than average A-level content. |
| Spec | 2.03a Mutually exclusive and independent events2.03d Calculate conditional probability: from first principles |
In a large examination room each candidate has just one electronic calculator.
\begin{itemize}
\item $G$ is the event that a randomly chosen candidate has a graphical calculator.
\item $T$ is the event that a randomly chosen candidate has a 'Texio' brand calculator.
\end{itemize}
You are given the following probabilities.
$$\text{P}(G) = 0.65 \quad \text{P}(T) = 0.4 \quad \text{P}(G \cap T) = 0.25$$
\begin{enumerate}[label=(\roman*)]
\item Are the events $G$ and $T$ independent? Justify your answer with an appropriate calculation. [2]
\item Find P($T | G$) and explain, in the context of this question, what this probability represents. [3]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2013 Q3 [5]}}