Statement - I : If A and B are two independen | vedclass

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(A) For two independent events $A$ and $B$,the conditional probability is defined as $P(A|B) = \frac{P(A \cap B)}{P(B)}$.Since $A$ and $B$ are indepen

Vedclass · Accepted Answer

Statement $- I$ is true. Statement $- II$ is true. Statement $- II$ is the correct explanation for Statement $- I$.

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(A) For two independent events $A$ and $B$,the conditional probability is defined as $P(A|B) = \frac{P(A \cap B)}{P(B)}$.Since $A$ and $B$ are independent,$P(A \cap B) = P(A) 	imes P(B)$.Therefore,$P(A|B) = \frac{P(A) 	imes P(B)}{P(B)} = P(A)$.This proves that Statement $- II$ is true.Given $P(A) = 1/2$ and $P(B) = 1/5$,since $A$ and $B$ are independent,$P(A|B) = P(A) = 1/2$.Thus,Statement $- I$ is also true.Since Statement $- I$ is derived directly from the property stated in Statement $- II$,Statement $- II$ is the correct explanation for Statement $- I$.

Statement $- I :$ If $A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/5$,then $P(A|B) = 1/2$.
Statement $- II : P(A|B) = P(A)$ if $A$ and $B$ are independent events.

Similar Questions

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Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$,then the probability of non-occurrence of at least one of the events $E$ and $F$ is

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If $A$ and $B$ are any two events of a random experiment and $P(B) \neq 1$,then $P(A | B^c) =$ ?

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Statement $- I :$ If $A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/5$,then $P(A|B) = 1/2$.Statement $- II : P(A|B) = P(A)$ if $A$ and $B$ are independent events.