Match List - I with List - II.
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List - I |
List – II |
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(A) |
If A and B are mutually exclusive events, then $P(A \cup B)=$ |
(I) |
$ \frac{P(A \cap B)}{P(B)}, P(B) \neq 0$ |
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(B) |
If A and B are independent events, then $P(A \cap B)=$ |
(II) |
$\frac{P(A \cap B)}{P(A)}, P(A) \neq 0$ |
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(C) |
If A and B are two events of a sample space of an experiment, then $P(A / B)=$ |
(III) |
$P(A) . P(B)$ |
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(D) |
If A and B are two events of a sample space of an experiment, then $P(B / A)=$ |
(IV) |
$P(A)+P(B) $ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
(A) for A, B to be mutually exclusive
$P(A \cup B)=P(A)+P(B)+\underbrace{P(A \cup B)}_{\text { this should be 0 }}$ → (IV)
(B) A, B independent events $\Rightarrow P(A \cap B)$
$=P(A) . P(B)$ → (III)
(C) $P(A / B)=\frac{P(A \cap B)}{P(B)}, P(B) \neq 0$ → (I)
(D) $P(B / A)=\frac{P(A \cap B)}{P(A)}, P(A) \neq 0$ → (II)