5 The Venn diagram illustrates the occurrence of two events \(A\) and \(B\). \includegraphics[max width=\textwidth, alt={}, center]{64f25a40-d3bf-4212-b92e-655f980c702b-5_480_771_452_655} 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 \(\mathrm { P } ( B )\).

## Question 5:

Let $P(B) = x$

Using $P(A \cup B) = P(A) + P(B) - P(A \cap B)$:
$0.9 = 2x + x - 0.3$
$x = 0.4$, so $P(B) = 0.4$ | M1 correct set of equations; M1 correct solution | A1

5 The Venn diagram illustrates the occurrence of two events $A$ and $B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{64f25a40-d3bf-4212-b92e-655f980c702b-5_480_771_452_655}

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  Q5 [3]}}