A and B are two events such that P(A) neq 0. | vedclass

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(B) We are given that $P(A) 
eq 0$. The conditional probability is defined as $P(B \mid A) = \frac{P(A \cap B)}{P(A)}$.$(i)$ If $A \subset B$,then $A

Vedclass · Accepted Answer

$1$ and $0$

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(B) We are given that $P(A) 
eq 0$. The conditional probability is defined as $P(B \mid A) = \frac{P(A \cap B)}{P(A)}$.$(i)$ If $A \subset B$,then $A \cap B = A$. Therefore,$P(B \mid A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A)}{P(A)} = 1$.(ii) If $A \cap B = \phi$,then $P(A \cap B) = P(\phi) = 0$. Therefore,$P(B \mid A) = \frac{P(A \cap B)}{P(A)} = \frac{0}{P(A)} = 0$.Thus,the values are $1$ and $0$ respectively.

$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B \mid A)$ if: $(i)$ $A \subset B$ (ii) $A \cap B = \phi$.

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