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Probability

Short 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 Questions

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

0
$1 third$
$1 over 12$
$1 over 12$

297 Views

Short Answer Type

733.

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

505 Views

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).

215 Views

735. Compute P(A|B), if P(B) = 0.5 and P(A ∩ B) = 0.32.

103 Views

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

(i) Since A is a subset of B

therefore space space space space space straight A space intersection thin space straight B space equals space straight A

...(1)
Now

straight P left parenthesis straight B space left enclose straight A right parenthesis end enclose space equals space fraction numerator straight P left parenthesis straight B intersection straight A right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction space equals space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction space equals space fraction numerator straight P left parenthesis straight A right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction

open square brackets because space of space left parenthesis 1 right parenthesis close square brackets

therefore space space space space straight P left parenthesis straight B space left enclose straight A right parenthesis end enclose space equals space 1

(ii)

straight P left parenthesis straight B space left enclose straight A right parenthesis end enclose space equals space fraction numerator straight P thin space left parenthesis straight B intersection straight A right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction space equals space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction

equals space fraction numerator straight P left parenthesis straight ϕ right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space space straight A space intersection straight B space equals straight ϕ space left parenthesis given right parenthesis close square brackets space equals space fraction numerator 0 over denominator straight P left parenthesis straight A right parenthesis end fraction space equals space 0

127 Views

738.

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