Q226 / 270 · NDA 2013 (Phase 2) · Mathematics

If three events $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are mutually exclusive, then which one of the following is correct?

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

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 $1 \leq i, j \leq m$.

Hence, the correct answer is option: 'C'.

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