If A and B are two independent events,then th | vedclass

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(A) We know that the probability of occurrence of at least one of $A$ and $B$ is $P(A \cup B)$.By the addition theorem of probability,$P(A \cup B) = P

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True

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(A) We know that the probability of occurrence of at least one of $A$ and $B$ is $P(A \cup B)$.By the addition theorem of probability,$P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Since $A$ and $B$ are independent events,$P(A \cap B) = P(A) P(B)$.Thus,$P(A \cup B) = P(A) + P(B) - P(A) P(B)$.We can write $P(A) = 1 - P(A')$,so:$P(A \cup B) = 1 - P(A') + P(B) - (1 - P(A')) P(B)$$= 1 - P(A') + P(B) - P(B) + P(A') P(B)$$= 1 - P(A') + P(A') P(B)$$= 1 - P(A') [1 - P(B)]$$= 1 - P(A') P(B')$.Therefore,the statement is true.

If $A$ and $B$ are two independent events,then the probability of occurrence of at least one of $A$ and $B$ is given by $1 - P(A') P(B')$. Is this statement true or false?

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