Events A and B are such that  State whether A and B are indepe

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 Multiple Choice QuestionsShort Answer Type

791. If P(not A) = 0.4, P(A ∪ B) = 0.75 and A, B are given to be independent events, find the value of P(B).
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792. If P(not B) = 0.65, P( A ∪ B) = 0.85 and A, B are independent events, find the value of P(A).
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793.

For two events A and B, let P(A) = 0.4 and P(B) = p and P(A∪ B) = 0.6
(i) Find p so that A and B are independent events.
(ii) Find p so that A and B are mutually exclusive events.

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794. Given that the events A and B are such that P(A) =1 half comma   straight P left parenthesis straight A union straight B right parenthesis space equals space 3 over 5 space and space straight P left parenthesis straight B right parenthesis space equals space straight p. Find p if they are mutually exclusive.

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795. Given that the events A and B are such that P(A) =1 half comma   straight P left parenthesis straight A union straight B right parenthesis space equals space 3 over 5 space and space straight P left parenthesis straight B right parenthesis space equals space straight p. Find p if they are independent.

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796.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find P(A ∩ B)

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797.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find P(A ∪ B)

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798.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find P(A|B) 

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799.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find P(B | A)

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800. Events A and B are such that straight P left parenthesis straight A right parenthesis space equals space 1 half comma space straight P left parenthesis straight B right parenthesis space equals space 7 over 12 space and space straight P left parenthesis not space straight A space or space not space straight B right parenthesis space equals 1 fourth. State whether A and B are independent?


straight P left parenthesis straight A right parenthesis space equals space 1 half comma space space straight P left parenthesis straight B right parenthesis space equals space 7 over 12
Now P(not A or not B) = 1 fourth space space space rightwards double arrow space space space space straight P left parenthesis straight A to the power of straight c space or space space straight B to the power of straight c right parenthesis space equals space 1 fourth
rightwards double arrow space space space space straight P left parenthesis straight A to the power of straight c space union space straight B to the power of straight c right parenthesis space equals space 1 fourth space space space rightwards double arrow space space space space straight P open square brackets left parenthesis straight A space intersection space straight B right parenthesis to the power of straight c close square brackets space equals space 1 fourth
rightwards double arrow space space space space 1 minus space straight P left parenthesis straight A space intersection space straight B right parenthesis space equals space 1 fourth space space space space rightwards double arrow space space space straight P left parenthesis straight A space intersection straight B right parenthesis space equals space 1 minus 1 fourth space equals space 3 over 4

Also,    straight P left parenthesis straight A right parenthesis space cross times space straight P left parenthesis straight B right parenthesis space equals space 1 half cross times 7 over 12 space equals space 7 over 24 not equal to 3 over 4

space space space space straight P left parenthesis straight A right parenthesis space cross times space straight P left parenthesis straight B right parenthesis space equals space 1 half cross times 7 over 12 space equals 7 over 24 not equal to 3 over 4

therefore space space space space straight P left parenthesis straight A right parenthesis space cross times space straight P left parenthesis straight B right parenthesis space space not equal to space straight P left parenthesis straight A intersection straight B right parenthesis

∴ A and B are not independent.
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