An experiment involves rolling a pair of dice and recording the number that comes up. Describe the following events.
A: the sum is greater than 8
B: 2 occurs on either die
C: The sum is at least 7 and multiple of 3.
Which pairs of these events are mutually exclusive?

Solution:

When a pair of dice is rolled, the sample space is given by

S = {(x, y) : x, y ∈ {1, 2, 3, 4, 5, 6} }

i.e.,

      {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

      (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

S = (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

      (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

      (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

      (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Given that A: the sum is greater than 8 B: 2 occurs on either die

So A = {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

Given that B: 2 occurs on either die

So B = {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}

Given that C: The sum is at least 7 and multiple of 3.

C = {(3, 6), (4, 5), (5, 4), (6, 3), (6, 6)}

It can be observed that

A ∩ B = Φ

B ∩ C = Φ

C ∩ A = {(3, 6), (4, 5), (5, 4), (6, 3), (6, 6)} ≠ Φ

Hence events A and B and events B and C are mutually exclusive

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NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.2 Question 3

An experiment involves rolling a pair of dice and recording the number that comes up. Describe the following events. A: the sum is greater than 8 B: 2 occurs on either die C: The sum is at least 7 and multiple of 3. Which pairs of these events are mutually exclusive?

Summary:

We found that

• A = {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
• B = {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}
• C = {(3, 6), (4, 5), (5, 4), (6, 3), (6, 6)}

Also, A and B and events B and C pairs are mutually exclusive