# 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?

$When\;a\;dice\;is\;rolled\;a\;sample\;space\;is\;given\;by\\*\left \{ 1,2,3,4,5,6 \right \}\\*Now,\;according\;to\;the\;question\;E=\left \{ 4 \right \}\;and\;F=\left \{ 2,4,6 \right \}\\*We\;can\;clearly\;see\;that\\*E\cap F=\left \{ 4 \right \}\ne \phi \\*Hence,\;E\;and\;F\;are\;not\;mutually\;exclusive\;events.$

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