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

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(B) Since $A \cap \bar B$ and $A \cap B$ are mutually exclusive events such that $A = (A \cap \bar B) \cup (A \cap B)$.Therefore,$P(A) = P(A \cap \bar

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Also independent

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(B) Since $A \cap \bar B$ and $A \cap B$ are mutually exclusive events such that $A = (A \cap \bar B) \cup (A \cap B)$.Therefore,$P(A) = P(A \cap \bar B) + P(A \cap B)$.This implies $P(A \cap \bar B) = P(A) - P(A \cap B)$.Since $A$ and $B$ are independent,$P(A \cap B) = P(A)P(B)$.Substituting this,we get $P(A \cap \bar B) = P(A) - P(A)P(B) = P(A)(1 - P(B))$.Since $P(\bar B) = 1 - P(B)$,we have $P(A \cap \bar B) = P(A)P(\bar B)$.Thus,$A$ and $\bar B$ are also independent.

If $A$ and $B$ are two independent events,then $A$ and $\bar B$ are

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