Let E_1, E_2, E_3 be three arbitrary events o | vedclass

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(C) For three events $E_1, E_2, E_3$:$1.$ $P(	ext{only one of them occurs}) = P(E_1\bar{E}_2\bar{E}_3 + \bar{E}_1E_2\bar{E}_3 + \bar{E}_1\bar{E}_2E_3

Vedclass · Accepted Answer

$P(	ext{at least one of them occurs}) = P(E_1 \cup E_2 \cup E_3)$

Vedclass · Answer

(C) For three events $E_1, E_2, E_3$:$1.$ $P(	ext{only one of them occurs}) = P(E_1\bar{E}_2\bar{E}_3 + \bar{E}_1E_2\bar{E}_3 + \bar{E}_1\bar{E}_2E_3)$. Option $(A)$ is incorrect as it lists the probability of exactly two events occurring.$2.$ $P(	ext{none of them occurs}) = P(\bar{E}_1 \cap \bar{E}_2 \cap \bar{E}_3) 
eq P(\bar{E}_1 + \bar{E}_2 + \bar{E}_3)$. Option $(B)$ is incorrect.$3.$ $P(	ext{at least one of them occurs}) = P(E_1 \cup E_2 \cup E_3)$. This is the definition of the union of events. Option $(C)$ is correct.$4.$ $P(	ext{all three occur}) = P(E_1 \cap E_2 \cap E_3) 
eq P(E_1 + E_2 + E_3)$. Option $(D)$ is incorrect.Therefore,the correct statement is $(C)$.

Let $E_1, E_2, E_3$ be three arbitrary events of a sample space $S$. Which of the following statements is correct?

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