If  find P(A ∩ B) if A and B are independent events. from

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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

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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.


Here,   straight P left parenthesis straight A right parenthesis space equals 3 over 5 comma space space straight P left parenthesis straight B right parenthesis space equals space 1 fifth                              ...(1)
Since A and B are independent events
therefore space space space space space space space space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals straight P left parenthesis straight A right parenthesis space straight P left parenthesis straight B right parenthesis space equals space 3 over 5 cross times 1 fifth space space space space space space space space space space space space space space space space space space space space left square bracket because space of space left parenthesis 1 right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 3 over 25

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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
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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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