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Independent Events

Two dice are ...

Question

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.

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Solution

(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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Similar questions

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A :

getting an even number on the first die.

B :

getting an odd number on the first die.

C :

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\leq 5

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Two dice are thrown. The events A, B, C, D, E and F are described as follows :

A = Getting an even number on the first die.

B = Getting an odd number on the first die.

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Refer to question 6 above, state true or false (give reason for your answer)
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A: getting an even number on the first die.

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(iii) two events A and B which are not mutually exclusive.
(iv) two events A and B which are mutually exclusive but not exhaustive.

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