If three events $X, Y, Z$ are mutually exclusive and exhaustive where $P(X) = \dfrac{2}{3} P(Y)$, $P(Z) = \dfrac{1}{3} P(Y)$, then $P(Z)$ is equal to (a) $\dfrac{1}{6}$ (b) $\dfrac{1}{3}$ (c) $\dfrac{5}{6}$ (d) $\dfrac{2}{3}$

If three events X, Y, Z are mutually exclusive and exhaustive where P(X) = (2)/(3) P(Y), P(Z) = (1)/(3) P(Y),

Question 68 of 73

X, Y, Z

(a)

\dfrac{1}{6}

(b)

\dfrac{1}{3}

(c)

\dfrac{5}{6}

(d)

\dfrac{2}{3}

West Bengal WbchseWest Bengal HS (WBCHSE) Board 2026MCQ· 1mImportance★★★★★

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Mutually exclusive and exhaustive means probabilities sum to $1$ ; express all in terms of $P(Y)$ .

The axiom that exhaustive mutually-exclusive events have total probability $1$ is a CBSE/NCERT Class 12 probability fundamental.

Let $P(Y)=t$ . Then $P(X)=\tfrac23 t$ and $P(Z)=\tfrac13 t$ . Since the events are mutually exclusive and exhaustive, …