Choose the correct answer from the given four options.If two even… - Vidyadip

MCQ

Choose the correct answer from the given four options.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.
✓
None of the above is correct.

✓

Answer

Correct option: D.

None of the above is correct.

If two events $A$ and $B$ are independent, then we know that
$\text{P}(\text{A}\cap\text{B})=\text{P}(\text{A})\cdot\text{P}(\text{B}),\text{P}(\text{A})\neq0,\text{P}(\text{B})\neq0$
Since, $A$ and $B$ have a common outcome.
Further, mutually exclusive events never have a common outcome.
In other words, two independents events having non $-$ zero probabilities of occurrence cannot be mutually exclusive and conversely, i.e., two mutually exclusive events having non $-$ zero probabilities of outcome cannot be independent.

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