Two events A and B will be independent if | vedclass

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Question

(B) Two events $A$ and $B$ are independent if and only if the occurrence of one does not affect the probability of the other. If $A$ and $B$ are indep

Vedclass · Accepted Answer

$P(A^{\prime} \cap B^{\prime}) = (1 - P(A))(1 - P(B))$

Vedclass · Answer

(B) Two events $A$ and $B$ are independent if and only if the occurrence of one does not affect the probability of the other. If $A$ and $B$ are independent,then their complements $A^{\prime}$ and $B^{\prime}$ are also independent. By the definition of independent events,the probability of the intersection of two independent events is the product of their individual probabilities. Therefore,$P(A^{\prime} \cap B^{\prime}) = P(A^{\prime}) \cdot P(B^{\prime})$. Since $P(A^{\prime}) = 1 - P(A)$ and $P(B^{\prime}) = 1 - P(B)$,we have $P(A^{\prime} \cap B^{\prime}) = (1 - P(A))(1 - P(B))$. Thus,option $B$ is the correct condition for independence.

Two events $A$ and $B$ will be independent if

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