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?

Question

Philoid · Accepted Answer

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.