A die is rolled. Let $E$ be the event "die shows $4$ " and $F$ be the event "die shows even number". Are $E$ and $F$ mutually exclusive ?
A die is rolled. Let $E$ be the event "die shows $4$ " and $F$ be the event "die shows even number". Are $E$ and $F$ mutually exclusive ?
When a die is rolled, the sample space is given by
$S =\{1,2,3,4,5,6\}$
Accordingly, $E =\{4\}$ and $F =\{2,4,6\}$
It is observed that $E \cap F=\{4\} \neq \phi$
Therefore, $E$ and $F$ are not mutually exchasive events.
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