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

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$\Large\fbox{\color{purple}{QUESTION}}$

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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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

➡️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.

$\Large\mathcal\green{FOLLOW \: ME}$

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Answer 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.