If three events A, B, C are mutually exclusive, then which one of...

If three events

\mathrm{A}, \mathrm{B}, \mathrm{C}

are mutually exclusive, then which one of the following is correct?

Options

A $\mathrm{P}(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C})=0$
B $\mathrm{P}(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C})=1$
C $\mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=0$
D $\mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=1$

Correct answer

C. $\mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=0$

Step-by-step solution

A set of events is said to be mutually exclusive if the occurrence of one of them precludes the occurrence of any of the remaining events. In set theory notation, events

\mathrm{A}_1, \mathrm{ A}_2, \mathrm{ A}_3 \ldots \ldots. \mathrm{A}_m

are mutually exclusive if

\mathrm{A}_i \cap \mathrm{ A}_j=\phi

for

i \neq j

and

1 \leq i, j \leq m

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