Events A and B are given to be independent. Find P(B), if it is

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 Multiple Choice QuestionsMultiple Choice Questions

781. If A and B are two events, such that P(A) ≠ 0 and P(B | A) = 1, then
  • A ⊂ B 
  • B ⊂ A
  • B = ϕ
  • B = ϕ
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782. If P( A|B) > P(A), then which of the following is correct:
  • P(B|A) < P(B) 
  • P(A ∩ B) < P(A) . P(B)
  • P(B|A) > P(B)
  • P(B|A) > P(B)
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783. If A and B are any two events such that P(A) + P(B) - P(A and B) = P(A), then
  • P(B|A) = 1
  • P(A|B) = 1
  • P(B|A) = 0
  • P(B|A) = 0
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784. If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is correct?
  • straight P left parenthesis straight A vertical line straight B right parenthesis space equals space fraction numerator straight P left parenthesis straight B right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction
  • straight P left parenthesis straight A vertical line straight B right parenthesis space less than thin space straight P left parenthesis straight A right parenthesis
  • straight P left parenthesis straight A vertical line straight B right parenthesis space greater or equal than space straight P left parenthesis straight A right parenthesis
  • straight P left parenthesis straight A vertical line straight B right parenthesis space greater or equal than space straight P left parenthesis straight A right parenthesis
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 Multiple Choice QuestionsShort Answer Type

785.

If straight P left parenthesis straight A right parenthesis space equals space 3 over 5 space and space straight P left parenthesis straight B right parenthesis space equals space 1 fifth comma find P(A ∩ B) if A and B are independent events.

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786.

Let E and F be events with straight P left parenthesis straight E right parenthesis space equals space 3 over 5 comma space straight P left parenthesis straight F right parenthesis space equals space 3 over 10 space and space straight P left parenthesis straight E space intersection space straight F right parenthesis space equals space 1 fifth. Are E and F independent?

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787. If P(A) = 0.38, P(A ∪ B) = 0.69, find P(B), if A and B are independent events. 
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788.

The events E and F are given to be independent. Find P(F) if it is given that  P(E) = 0.35 and P(E ∪ F) = 0.60.

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789. Events A and B are given to be independent. Find P(B), if it is given that P(A) = 0.40, P(A ∪ B) = 0.70


P(A) = 0.40, P(A ∪ B) = 0.70
Now    straight P left parenthesis straight A space union thin space straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space plus space straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A intersection straight B right parenthesis
rightwards double arrow space space space space space space space straight P left parenthesis straight A union straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis plus space straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A right parenthesis thin space straight P left parenthesis straight B right parenthesis space space space left square bracket because space space straight A comma space straight B space and space independent space events right square bracket
rightwards double arrow space space space space space space space space space space space 0.70 space equals space 0.40 plus space straight P left parenthesis straight B right parenthesis space minus space left parenthesis 0.40 right parenthesis thin space straight P left parenthesis straight B right parenthesis
rightwards double arrow space space space space space space space space space space space 0.30 space equals space left parenthesis 0.60 right parenthesis thin space straight P left parenthesis straight B right parenthesis
rightwards double arrow space space space space space space space space space space space space straight P left parenthesis straight B right parenthesis space equals space fraction numerator 0.30 over denominator 0.60 end fraction space equals space 0.5

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790.

If A and B are two independent events such that P(A ∪ B) = 0.6 and P(A) = 0.2, find P(B).

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