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  • 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

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

Answers (1)

Events which cannot happen at the same time are known as mutually exclusive events. 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.

Therefore, if A and B events are independent, any information about A cannot tell anything about B while if they are mutually exclusive then we know if A occurs B does not occur.
Therefore, independent events cannot be mutually exclusive.
To test if probability of independent events is 1 or not:

Let A be the event of obtaining a head.
P(A) = 1/2

Let B be the event of obtaining 5 on a die.
P(B) = 1/6
Now A and B are independent events.

\begin{aligned} &\text { Therefore, } \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})=\frac{1}{2}+\frac{1}{6}\\ &=\frac{3+1}{12}=\frac{4}{12}\\ &=\frac{1}{3}\\ &\text { Hence } P(A)+P(B) \neq 1\\ &\text { It is true in every case when two events are independent. } \end{aligned}

Hence option D is correct.

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infoexpert22

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