# 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?

**Solution:**

Two events are said to be mutually exclusive if they have no common element.

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

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

According to the given problem, E is the event “die shows 4”. So E = {4}

and F is the event “die shows even number”. So F = {2, 4, 6}

It is observed that E ∩ F = {4} ≠ ϕ

Therefore, E and F are not mutually exclusive events

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.2 Question 1

## 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?

**Summary:**

A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Then E and F are not mutually exclusive events

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