If P(A) = 0.38, P(A ∪ B) = 0.69, find P(B), if A and B are ind

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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. 


Here,   P(A) = 0.38,   straight P left parenthesis straight A union straight B right parenthesis space equals space 0.69
Let P(B) = p
Since A and B are independent.
therefore          straight P left parenthesis straight A space intersection thin space straight B right parenthesis space equals straight P left parenthesis straight A right parenthesis space cross times space straight P left parenthesis straight B right parenthesis
therefore space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space left parenthesis 0.38 right parenthesis thin space straight p                                   ...(1)

Now straight P left parenthesis straight A space union 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.

therefore space space space 0.69 space equals space 0.38 space plus space straight p space minus space left parenthesis 0.38 right parenthesis thin space straight p
therefore space space space 0.31 space equals space 0.62 space straight p space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space straight p space equals space fraction numerator 0.31 over denominator 0.62 end fraction
therefore space space space space space straight p space equals space 31 over 62 space equals space 1 half
therefore space space space straight P left parenthesis straight B right parenthesis space equals 1 half space equals space 0.5


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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
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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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