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 the die is rolled the sample space will consist of following outcomes


S = (1, 2, 3, 4, 5, 6)


According to the given conditions


E = (4) and


(F) = (2, 4, 6)


E ∩ F = (4) ∩ (2, 4, 6)


⇒ (4) ≠ ϕ as there is a common element between E & F


Hence E and F are not mutually exclusive event.


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