If . from Mathematics Probability

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 Multiple Choice QuestionsShort Answer Type

731. If each element of a second order determinant is either zero or one, what is the probability that the value of determinant is positive? (Assume that the individual enteries of the determinant are chosen independently, each value being assumed with probability 1 half right parenthesis.
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 Multiple Choice QuestionsMultiple Choice Questions

732. The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
  • 0

  • 1 third
  • 1 over 12
  • 1 over 12
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 Multiple Choice QuestionsShort Answer Type

733.

If straight P left parenthesis straight A right parenthesis space equals space 7 over 13 comma space straight P left parenthesis straight B right parenthesis space equals space 9 over 13 comma space space straight P left parenthesis straight A intersection straight B right parenthesis space equals 4 over 13 comma space evaluate space straight P left parenthesis straight A space left enclose straight B right parenthesis.

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734. Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P(E | F) and P(F | E).
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735. Compute P(A|B), if P(B) = 0.5 and P(A ∩ B) = 0.32.
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736.

Evaluate straight P left parenthesis straight A union straight B right parenthesis comma space space if space 2 space straight P left parenthesis straight A right parenthesis space equals space straight P left parenthesis straight B right parenthesis space equals 5 over 13 space and space straight P left parenthesis straight A space left enclose straight B right parenthesis space equals 2 over 5.

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737. A and B are two events such that P(A) ≠ 0. Find P (B|A), if
(i) A is a subset of B      (ii) A ∩ B = ϕ
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738.

If straight P left parenthesis straight A right parenthesis space equals space 6 over 11 comma space space space straight P left parenthesis straight B right parenthesis space equals space 5 over 11 space space and space straight P left parenthesis straight A space union space straight B right parenthesis space equals space 7 over 11 comma space space find space straight P left parenthesis straight A intersection straight B right parenthesis.


Here  straight P left parenthesis straight A right parenthesis space equals space 6 over 11 comma space space straight P left parenthesis straight B right parenthesis space equals space 5 over 11 comma space space straight P left parenthesis straight A union straight B right parenthesis space equals space 7 over 11

 Now      straight P left parenthesis straight A union 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 space space space space space space space space space space space space 7 over 11 space equals space 6 over 11 plus 5 over 11 minus space straight P left parenthesis straight A space intersection space straight B right parenthesis
rightwards double arrow space space space space space space space space space space space space space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 6 over 11 plus 5 over 11 minus 7 over 11 space equals space fraction numerator 6 plus 5 minus 7 over denominator 11 end fraction space equals 4 over 11


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739.

If straight P left parenthesis straight A right parenthesis space equals space 6 over 11 comma space space space straight P left parenthesis straight B right parenthesis space equals space 5 over 11 space space and space straight P left parenthesis straight A space union space straight B right parenthesis space equals space 7 over 11 comma space space find space straight P left parenthesis straight A space left enclose straight B right parenthesis.

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740.

If straight P left parenthesis straight A right parenthesis space equals space 6 over 11 comma space space space straight P left parenthesis straight B right parenthesis space equals space 5 over 11 space space and space straight P left parenthesis straight A space union space straight B right parenthesis space equals space 7 over 11 comma space space find space straight P left parenthesis straight B space left enclose straight A right parenthesis.

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