Three Events with Independence Constraints

A question is this type if and only if it involves three events where some pairs are independent, some are mutually exclusive, or other special relationships are specified, requiring you to find unknown probabilities.

3 questions · Standard +0.0

2.03a Mutually exclusive and independent events 2.03c Conditional probability: using diagrams/tables

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Edexcel AS Paper 2 2019 June Q2

5 marks Standard +0.8

The Venn diagram shows three events, $A$, $B$ and $C$, and their associated probabilities. \includegraphics[max width=\textwidth, alt={}, center]{e73193ee-339e-48ab-811c-9ab6817f786d-04_680_780_296_644}

Events $B$ and $C$ are mutually exclusive.
Events $A$ and $C$ are independent.
Showing your working, find the value of $x$, the value of $y$ and the value of $z$.

Edexcel S1 2013 January Q7

12 marks Moderate -0.3

Given that

$$\mathrm { P } ( A ) = 0.35 , \quad \mathrm { P } ( B ) = 0.45 \quad \text { and } \quad \mathrm { P } ( A \cap B ) = 0.13$$ find

$\mathrm { P } ( A \cup B )$
$\mathrm { P } \left( A ^ { \prime } \mid B ^ { \prime } \right)$ The event $C$ has $\mathrm { P } ( C ) = 0.20$ The events $A$ and $C$ are mutually exclusive and the events $B$ and $C$ are independent.
Find $\mathrm { P } ( B \cap C )$
Draw a Venn diagram to illustrate the events $A , B$ and $C$ and the probabilities for each region.
Find $\mathrm { P } \left( [ B \cup C ] ^ { \prime } \right)$

Edexcel S1 2009 June Q7

7 marks Moderate -0.5

7. (a) Given that $\mathrm { P } ( A ) = a$ and $\mathrm { P } ( B ) = b$ express $\mathrm { P } ( A \cup B )$ in terms of $a$ and $b$ when

$A$ and $B$ are mutually exclusive,
$A$ and $B$ are independent. Two events $R$ and $Q$ are such that $\mathrm { P } \left( R \cap Q ^ { \prime } \right) = 0.15 , \quad \mathrm { P } ( Q ) = 0.35$ and $\mathrm { P } ( R \mid Q ) = 0.1$ Find the value of
(b) $\mathrm { P } ( R \cup Q )$,
(c) $\mathrm { P } ( R \cap Q )$,
(d) $\mathrm { P } ( R )$.