Mathematics20251 markAssertion-reasonProbabilityTool: Venn diagram generator and visualiser

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If E₁ and E₂ are two mutually exclusive events associated with a random experiment and E is an…

Assertion: If $E_1$ and $E_2$ are two mutually exclusive events associated with a random experiment and $E$ is an event such that $P(E) \neq 0$, then $P\left(\frac{E_1 \cup E_2}{E}\right) = P\left(\frac{E_1}{E}\right) + P\left(\frac{E_2}{E}\right)$.

Reason: For two mutually exclusive events $E_1$ and $E_2$, $P(E_1 \cap E_2) = 0$.

If $E_1$ and $E_2$ are two mutually exclusive events associated with a random experiment and $E$ is an event such that: $P(E) \neq 0$. Assertion (A): $P\left(\frac{E_1 \cup E_2}{E}\right) = P\left(\frac{E_1}{E}\right) + P\left(\frac{E_2}{E}\right)$. Reason (R): For two mutually exclusive events $E_1$ and $E_2$, $P(E_1 \cap E_2) = 0$.

(a)Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation for Assertion (A).
(b)Both Assertion (A) and Reason (R) are true, but Reason (A) is not the correct explanation for Assertion (A).
(c)Assertion (A) is true, and Reason (R) is false.
(d)Assertion (A) is false, and Reason (R) is true.

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Answer

Official answer key

Correct option: (a)

Answer: (a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation for Assertion (A).