Question

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?

Answer 1

Sample Space:

When a die is rolled,
S = {1, 2, 3, 4, 5, 6}

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Given Events:

E: Die shows 4
E = {4}

F: Die shows an even number
F = {2, 4, 6}

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Check for mutual exclusiveness:

E ∩ F = {4}

Since E ∩ F ≠ ∅,

E and F are not mutually exclusive.

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Final Answer:

The events E and F are not mutually exclusive.