NCERT Solutions
Class 11 Maths
Probability

Ex.16.2 Q.7
Refer to question 6 above, state true or false: (give reason for your answer)
(1) A and B are mutually exclusive
(2) A and B are mutually exclusive and exhaustive
(3) A = B′
(4) A and C are mutually exclusive
(5) A and B′ are mutually exclusive.
(6) A′, B′, C are mutually exclusive and exhaustive.
A: getting an even number on the first die.
A = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
B: getting an odd number on the first die.
B = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}
C: getting the sum of the numbers on the dice ≤ 5
C = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}
(1) It is observed that A ∩ B = ф
So, A and B are mutually exclusive.
Thus, the given statement is true.
(2) It is observed that A ∩ B = ф and A ∪ B = S
So, A and B are mutually exclusive and exhaustive.
Thus, the given statement is true.
(3) It is observed that
B’ = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} = A
Thus, the given statement is true.
(4) It is observed that A ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} ≠ ф
So, A and C are not mutually exclusive.
Thus, the given statement is false.
(5) A ∩ B’ = A ∩ A = A
Since A ∩ B’ ≠ ф
So, A and B’ are not mutually exclusive.
Thus, the given statement is false.
(6) It can be observed that: A’ U B’ U C = S
However, B’ ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} ≠ ф
Therefore, events A’, B’ and C are not mutually exclusive and exhaustive.
Thus, the given statement is false.