Moderate -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 probability laws, but involves only routine algebraic manipulation with no conceptual surprises—slightly easier than average for A-level.
3 The Venn diagram illustrates the occurrence of two events \(A\) and \(B\).
\includegraphics[max width=\textwidth, alt={}, center]{b35b2b3b-0d26-4a35-b4d2-110bf270d5dc-2_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 \(\mathrm { P } ( B )\).
3 The Venn diagram illustrates the occurrence of two events $A$ and $B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{b35b2b3b-0d26-4a35-b4d2-110bf270d5dc-2_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 2005 Q3 [3]}}