NCERT Solutions
Class 11 Maths
Probability

Ex.16.2 Q.3
An experiment involves rolling a pair of dice and recording the numbers that come up.
Describe the following events:
A: the sum is greater than 8,
B: 2 occur on either die
C: the sum is at least 7 and a multiple of 3. Which pairs of these events are mutually exclusive?
When a pair of dice is rolled, the sample space is given by:
S = {(x, y): x comes from 1st dice and y comes from 2nd dice and x, y = 1, 2, 3, 4, 5, 6}
= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(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)}
A: the sum is greater than 8,
A = {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
B: 2 occur on either die
B = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (1, 2), (3, 2), (4, 2), (5, 2), (6, 2)}
C: the sum is at least 7 and a multiple of 3
C = {(3, 6), (4, 5), (5, 4), (6, 3), (6, 6)}
It is observed that
A ∩ B = ф
B ∩ C = ф
C ∩ A = {(3, 6), (4, 5), (5, 4), (6, 3), (6, 6)} ≠ ф
Hence, events A and B and events B and C are mutually exclusive.