Match the following If E1 and E2 are the mutually exclusive eventsAiE1- E2-E1If E1 and E2 are the mutually exclusive and exhaustive eventsBiiE1-E2- E1- E2-E1If E1 and E2 have common outcomes- thenCiiiE1- E2-E1- E2-SIf E1 and E2 are two events such that E1- E2DivE1- E2-

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Exhaustive Events

Match the fol...

Question

Match the following

If $E_{1}$ and $E_{2}$ are the mutually exclusive events
A i $E_{1} \cap E_{2} = E_{1}$

If $E_{1}$ and $E_{2}$ are the mutually exclusive and exhaustive events
B ii $(E_{1} - E_{2}) \cup (E_{1} \cap E_{2}) = E_{1}$

If $E_{1}$ and $E_{2}$ have common outcomes, then
C iii $E_{1} \cap E_{2} = ϕ, E_{1} \cup E_{2} = S$

If $E_{1}$ and $E_{2}$ are two events such that $E_{1} \subset E_{2}$
D iv $E_{1} \cap E_{2} = ϕ$

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Solution

(A) Hint: Use Set theoretic principles
Use the properties of mutually exclusive events

If $E_{1} & E_{2}$ are mutually exclusive events, then $E_{1} \cap E_{2} = ϕ$

(B) Use the properties of mutually exclusive & exhaustive events

If $E_{1} & E_{2}$ are mutually exclusive and exhaustive events, then

$E_{1} \cap E_{3} = ϕ & E_{1} \cup E_{2} = S$

(C) Hint: Use Venn diagram
Use Venn diagram
If $E_{1} & E_{2}$ have common outcomes, then $(E_{1} - E_{2}) \cup (E_{1} \cap E_{2}) = E_{1}$

(D)
Hint: Use Venn diagram
Use Venn diagram
If $E_{1} & E_{2}$ are two events such that
$E_{1} \subset E_{2} \Rightarrow E_{2} = E_{1}$

$(A) \to (i v), (B) \to (i i i), (C) \to (i i), (D) \to (i)$

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Exhaustive Events

Standard X Mathematics

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If $E_{1}$ and $E_{2}$ are the mutually exclusive events	A	i	$E_{1} \cap E_{2} = E_{1}$
If $E_{1}$ and $E_{2}$ are the mutually exclusive and exhaustive events	B	ii	$(E_{1} - E_{2}) \cup (E_{1} \cap E_{2}) = E_{1}$
If $E_{1}$ and $E_{2}$ have common outcomes, then	C	iii	$E_{1} \cap E_{2} = ϕ, E_{1} \cup E_{2} = S$
If $E_{1}$ and $E_{2}$ are two events such that $E_{1} \subset E_{2}$	D	iv	$E_{1} \cap E_{2} = ϕ$