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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 $1 half right parenthesis.$

There are four entries in determinant of 2 × 2 order. Each entry may be filled up in two ways with 0 or 1.
∴ number of determinants that can be formed = 2⁴ = 16
∴ total number of cases = 16
The value of determinant is positive in the cases
$open vertical bar table row 1 0 row 0 1 end table close vertical bar comma space open vertical bar table row 1 0 row 1 1 end table close vertical bar comma space open vertical bar table row 1 1 row 0 1 end table close vertical bar$
$therefore space space$ number of favourable cases = 3
$therefore$ the probability that the determinant is positive = $3 over 16.$

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

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

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739.

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740.

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