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Question
Let sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let us define the following events
A: "set of numbers divisible by 2".
B: "set of numbers divisible by 3".
Then what should be the event C such that events A, B and C are mutually exhaustive?
Let sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let us define the following events
A: "set of numbers divisible by 2".
B: "set of numbers divisible by 3".
Then what should be the event C such that events A, B and C are mutually exhaustive?
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Solution
The correct option is B {1, 5, 7}
A = {2, 4, 6, 8, 10}
B = {3, 6, 9}
⇒A∪B = {2, 3, 4, 6, 8, 9, 10}
Events A, B and C are mutually exhaustive when A∪B∪C=SSo, C=S−(A∪B)Therefore, C = {1, 5, 7}
A = {2, 4, 6, 8, 10}
B = {3, 6, 9}
⇒A∪B = {2, 3, 4, 6, 8, 9, 10}
Events A, B and C are mutually exhaustive when A∪B∪C=SSo, C=S−(A∪B)Therefore, C = {1, 5, 7}