| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Independence test requiring preliminary calculations |
| Difficulty | Moderate -0.8 This is a straightforward application of the independence test P(T|M) = P(T) and finding P(T∩M) using the conditional probability formula. The Venn diagram is routine bookwork. All steps are standard S1 procedures with no problem-solving insight required, making it easier than average. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
4 In a food survey, a large number of people are asked whether they like tomato soup, mushroom soup, both or neither. One of these people is selected at random.
\begin{itemize}
\item $T$ is the event that this person likes tomato soup.
\item $M$ is the event that this person likes mushroom soup.
\end{itemize}
You are given that $\mathrm { P } ( T ) = 0.55 , \mathrm { P } ( M ) = 0.33$ and $\mathrm { P } ( T \mid M ) = 0.80$.\\
(i) Use this information to show that the events $T$ and $M$ are not independent.\\
(ii) Find $\mathrm { P } ( T \cap M )$.\\
(iii) Draw a Venn diagram showing the events $T$ and $M$, and fill in the probability corresponding to each of the four regions of your diagram.
\hfill \mbox{\textit{OCR MEI S1 2012 Q4 [6]}}