## 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

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?​

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1 month 2021-08-16T14:44:08+00:00 2 Answers 0 views 0

## Answers ( )

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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?

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➡️Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.

➡️So, S = (1, 2, 3, 4, 5, 6)

➡️As per the conditions given the question

As per the conditions given the questionE be the event “die shows 4”

➡️E = (4)

➡️F be the event “die shows even number”

➡️F = (2, 4, 6)

➡️E∩F = (4) ∩ (2, 4, 6)

➡️= 4

➡️4 ≠ φ … [because there is a common element in E and F]

➡️Therefore E and F are not mutually exclusive event.

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2. When a die is rolled the sample space is given by,

S={1,2,3,4,5,6}

Now according to question E={4} and F={2,4,6}

Clearly  E∩F={4}=ϕ

Hence, E and F are not mutually exclusive events.