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Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5
State true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii)
(iv) A and C are mutually exclusive
(v) A and are mutually exclusive
(vi) are mutually exclusive and exhaustive.
(i) It is observed that A ∩ B = Φ
∴ A and B are mutually exclusive.
Thus, the given statement is true.
(ii) It is observed that A ∩ B = Φ and A ∪ B = S
∴ A and B are mutually exclusive and exhaustive.
Thus, the given statement is true.
(iii) It is observed that
Thus, the given statement is true.
(iv) It is observed that A ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} ≠Φ
∴A and C are not mutually exclusive.
Thus, the given statement is false.
(v)
∴A and are not mutually exclusive.
Thus, the given statement is false.
(vi) It is observed that;
However,
Therefore, events are not mutually exclusive and exhaustive.
Thus, the given statement is false.
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