Suppose A and B are two events with $$P(A)=0.5$$ and $$P(A$$∪$$B)=0.8$$. Let $$P(B)=p$$ if A and B are mutually exclusive and $$P(B)=q$$ if A and B are independent events then the value of $$q/p$$ is

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Suppose A and B are two events with $$P(A)=0.5$$ and $$P(A$$∪$$B)=0.8$$. Let $$P(B)=p$$ if A and B are mutually  exclusive and $$P(B)=q$$ if A and B are independent events  then the value of $$q/p$$ is

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When A and B are mutually exclusive, $$P(A$$∩$$B)=0$$∴    $$P(A$$∪$$B)=P(A)+P(B)----1$$⇒    $$0.8=0.5+p$$⇒    $$p=0.3$$    $$P(A$$∪$$B)=P(A)+P(B)----2$$    $$=P(A)+P(B)$$−$$P(A$$∩$$B)$$    $$=P(A)+P(B)$$−$$P(A)P(B)$$⇒    $$0.8=0.5+q$$−$$(0.5)q$$⇒    $$0.3=q2$$⇒    $$q=0.6-----3$$⇒    $$q/p=2$$

Theorems of probability

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$Suppose A and B are two events with P (A) = 0.5 and$ $P (A \cup B) = 0.8 . Let P (B) = p if A and B are mutually$
$exclusive and P (B) = q if A and B are independent events then the value of q / p is$

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Theorems of probability

Remember concepts with our Masterclasses.

Suppose A and B are two events with P(A)=0.5 and P(A∪B)=0.8. Let P(B)=p if A and B are mutually exclusive and P(B)=q if A and B are independent events then the value of q/p is

When A and B are mutually exclusive, P(A∩B)=0∴ P(A∪B)=P(A)+P(B)----1⇒ 0.8=0.5+p⇒ p=0.3 P(A∪B)=P(A)+P(B)----2 =P(A)+P(B)−P(A∩B) =P(A)+P(B)−P(A)P(B)⇒ 0.8=0.5+q−(0.5)q⇒ 0.3=q2⇒ q=0.6-----3⇒ q/p=2

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$Suppose A and B are two events with P (A) = 0.5 and$ $P (A \cup B) = 0.8 . Let P (B) = p if A and B are mutually$
$exclusive and P (B) = q if A and B are independent events then the value of q / p is$