Question

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment A: ‘the sum is even’. B: ‘the sum is a multiple of 3’. C: ‘the sum is less than 4’. D: ‘the sum is greater than 11’. Which pairs of these events are mutually exclusive?

• A. A & B
• B. C & D
• C. B & C
• D. A & C

Answer 1

Answer:

B. C & D

A = {(1,1) (1,3) (1,5) (2, 2) (2 4) (2, 6) ( 3 1) (3 3) ( 3 5) (4 2) (4 4) ( 4 6) ( 5 1) (5 3) ( 5 5) (6 2) ( 6 4) ( 6 6 )} B = {(1 2) ( 1 5) ( 2 1 ) ( 2 4) (3 3) ( 3 6) ( 4 2 ) (51) ( 6 6) ( 6 3) ( 4 5) (5 4)} C + { (1 1) (1 2) (2 1) } D = { ( 6 6)} A ∩ B ≠ φ A ∩ C ≠ φ A ∩ D ≠ φ B ∩ C ≠ φ B ∩ D ≠ φ C ∩ D = φ Two events A and B are called mutually exclusive events if the occurrence of any one of them excludes the occurrence of the other event, i.e., if they can not occur simultaneously. In this case the sets A and B are disjoint. Simple events of a sample space are always mutually exclusive.