| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Basic two-way table probability |
| Difficulty | Easy -1.2 This is a straightforward two-way table probability question requiring only reading values from the table and applying the basic conditional probability formula P(A|B) = P(A∩B)/P(B). All required values are directly given in the table with no calculation complexity beyond simple division. This is easier than average A-level content as it tests only basic probability reading and interpretation skills. |
| Spec | 2.03c Conditional probability: using diagrams/tables |
| \multirow{2}{*}{} | Weather Forecast | \multirow{2}{*}{Total} | |||
| Sunny | Cloudy | Wet | |||
| \multirow{3}{*}{Actual Weather} | Sunny | 55 | 12 | 7 | 74 |
| Cloudy | 17 | 128 | 29 | 174 | |
| Wet | 3 | 33 | 81 | 117 | |
| Total | 75 | 173 | 117 | 365 | |
1 An amateur weather forecaster describes each day as either sunny, cloudy or wet. He keeps a record each day of his forecast and of the actual weather. His results for one particular year are given in the table,
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{\multirow{2}{*}{}} & \multicolumn{3}{|c|}{Weather Forecast} & \multirow{2}{*}{Total} \\
\hline
& & Sunny & Cloudy & Wet & \\
\hline
\multirow{3}{*}{Actual Weather} & Sunny & 55 & 12 & 7 & 74 \\
\hline
& Cloudy & 17 & 128 & 29 & 174 \\
\hline
& Wet & 3 & 33 & 81 & 117 \\
\hline
\multicolumn{2}{|c|}{Total} & 75 & 173 & 117 & 365 \\
\hline
\end{tabular}
\end{center}
A day is selected at random from that year.\\
(i) Show that the probability that the forecast is correct is $\frac { 264 } { 365 }$.
Find the probability that\\
(ii) the forecast is correct, given that the forecast is sunny,\\
(iii) the forecast is correct, given that the weather is wet,\\
(iv) the weather is cloudy, given that the forecast is correct.
\hfill \mbox{\textit{OCR MEI S1 Q1 [8]}}