Q. 705.0( 1 Vote )

# If two events are independent, then

A. they must be mutually exclusive

B. the sum of their probabilities must be equal to 1

C. (A) and (B) both are correct

D. None of the above is correct

Correct

Answer :

**Mutually exclusive** are the events which cannot happen at the same time.

For example: when tossing a coin, the result can either be heads or tails but cannot be both.

Events are **independent** if the occurrence of one event does not influence (and is not influenced by) the occurrence of the other(s).

**Eg:** Rolling a die and flipping a coin. The probability of getting any number on the die will not affect the probability of getting head or tail in the coin.

So, if A and B are event is independents any information about A can not tell anything about B while if they are mutually exclusive then we know if A occurs B does not occur.

So independent events cannot be mutually exclusive.

Now to test if probability of independent events is 1 or not

Consider an example:

Let A be the event of obtaining a head.

P(A) = 1/2

B be the event of obtaining 5 on a die.

P(B) = 1/6

Now A and B are independent events.

So, P(A) + P(B)

Hence P(A) + P(B)≠ 1

It is true in every case when two events are independent.

Hence option D is correct.

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