| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Finding Unknown Probabilities in Venn Diagrams |
| Difficulty | Standard +0.3 This is a straightforward application of the inclusion-exclusion principle with one algebraic constraint. Students must set up equations using P(A∪B) = 1 - 0.1 = 0.9, P(A∩B) = 0.3, and P(A) = 2P(B), then solve a simple linear system. It requires understanding of Venn diagram regions and basic algebra, making it slightly easier than average for A-level. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables |
**(i) State two adjustments the company could make. [2]**
B1: Increase the mean weight
B1: Decrease the standard deviation
**(ii) Given that $\Sigma x = 11409$ and $\Sigma x^2 = 5206937$, calculate the sample mean and sample standard deviation of these weights. [3]**
M1: Sample mean $= \frac{\Sigma x}{n} = \frac{11409}{25}$
A1: Sample mean $= 456.36$ grams
M1: Sample standard deviation $= \sqrt{\frac{\Sigma x^2}{n} - (\bar{x})^2}$ or $\sqrt{\frac{\Sigma x^2 - \frac{(\Sigma x)^2}{n}}{n}}$
A1: Sample standard deviation $= 4.72$ grams (or 4.71 grams)
---3 The Venn diagram illustrates the occurrence of two events $A$ and $B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{1ad9c390-b42f-47d8-86c5-f73a42d97721-02_513_826_1713_658}
You are given that $\mathrm { P } ( A \cap B ) = 0.3$ and that the probability that neither $A$ nor $B$ occurs is 0.1 . You are also given that $\mathrm { P } ( A ) = 2 \mathrm { P } ( B )$.
Find $\mathrm { P } ( B )$.
\hfill \mbox{\textit{OCR MEI S1 Q3 [8]}}