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Experimental Probability

A die is roll...

Question

A die is rolled. Let $E$ be the event ''die shows $4$ '' and $F$ be the event ''die shows an even number''. Then which of the following statements is/are true about the events :

E \cup F = F

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E \cup F = E

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E

and

F

are not mutually exclusive events.

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E

and

F

are mutually exclusive events.

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Solution

The correct option is C $E$ and $F$ are not mutually exclusive events.
Let us assume that $1, 2, 3, 4, 5$ and $6$ are the possible outcomes when the die is thrown.
So, $S = {1, 2, 3, 4, 5, 6}$
As per the condition given;
$E$ be the event ''die shows 4''
$E = {4}$
$F$ be the event ''die shows an even number''
$F = {2, 4, 6}$
Clearly,
$E \cup F = {2, 4, 6} = F$
and $E \cap F = {4} \cap {2, 4, 6} = {4} \neq ϕ$
Therefore $E$ and $F$ are not mutually exclusive events.

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