Moderate -0.8 This is a straightforward S1 question testing basic probability definitions and rules. Part (a) requires simple Venn diagram shading, (b) applies the addition rule for mutually exclusive events and definition of conditional probability (which is zero), and (c) uses the addition rule for independent events to find P(G) then applies conditional probability. All parts involve direct application of standard formulas with no problem-solving insight required, making it easier than average.
2. (a) Shade the region representing the event \(A \cup B ^ { \prime }\) on the Venn diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{01259350-0119-4500-a81b-bfa1b4234559-06_355_563_306_694}
The two events \(C\) and \(D\) are mutually exclusive.
Given that \(\mathrm { P } ( C ) = \frac { 1 } { 5 }\) and \(\mathrm { P } ( D ) = \frac { 3 } { 10 }\) find
(b) (i) \(\quad \mathrm { P } ( C \cup D )\)
(ii) \(\mathrm { P } ( C \mid D )\)
The two events \(F\) and \(G\) are independent.
Given that \(\mathrm { P } ( F ) = \frac { 1 } { 6 }\) and \(\mathrm { P } ( F \cup G ) = \frac { 3 } { 8 }\) find
(c) (i) \(\mathrm { P } ( G )\)
(ii) \(\mathrm { P } \left( F \mid G ^ { \prime } \right)\)
2. (a) Shade the region representing the event $A \cup B ^ { \prime }$ on the Venn diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{01259350-0119-4500-a81b-bfa1b4234559-06_355_563_306_694}
The two events $C$ and $D$ are mutually exclusive.\\
Given that $\mathrm { P } ( C ) = \frac { 1 } { 5 }$ and $\mathrm { P } ( D ) = \frac { 3 } { 10 }$ find\\
(b) (i) $\quad \mathrm { P } ( C \cup D )$\\
(ii) $\mathrm { P } ( C \mid D )$
The two events $F$ and $G$ are independent.\\
Given that $\mathrm { P } ( F ) = \frac { 1 } { 6 }$ and $\mathrm { P } ( F \cup G ) = \frac { 3 } { 8 }$ find\\
(c) (i) $\mathrm { P } ( G )$\\
(ii) $\mathrm { P } \left( F \mid G ^ { \prime } \right)$
\hfill \mbox{\textit{Edexcel S1 2018 Q2 [8]}}