Evaluate  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.


              2 P(A) = P(B) = 5 over 13                             (given)
therefore space space space space space space straight P left parenthesis straight A right parenthesis space equals space 5 over 26 comma space space space straight P left parenthesis straight B right parenthesis space equals space 5 over 13

Also,    straight P left parenthesis straight A space left enclose straight B right parenthesis space equals space 2 over 5 space space space space space rightwards double arrow space space space space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals space 2 over 5 space space space rightwards double arrow space space space space space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator begin display style 5 over 13 end style end fraction space equals 2 over 5
therefore space space space space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 2 over 5 cross times 5 over 13 space equals space 2 over 13

Now,             straight P left parenthesis straight A union straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis plus straight P left parenthesis straight B right parenthesis minus straight P left parenthesis straight A intersection straight B right parenthesis

                                    equals space 5 over 26 plus 5 over 13 minus 2 over 13 space equals fraction numerator 5 plus 10 minus 4 over denominator 26 end fraction space equals 11 over 26



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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.

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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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