Friday, December 30, 2016

positive determinant from miscellaneous probability questions ncert cbse 12th mathematics

positive determinant and electronic assembly with two subsystems question from miscellaneous probability questions ncert cbse 12th mathematics

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive?

There are 4 entries in the second order determinant ,each of which can be filled in two ways with either 0 or 1
Such determinants can be constructed in 24 ways ( (2^4) ways)
Therefore if S is the sample space n(S) = (2^4) = 16
Let E be the event that the value of the selected determinant is positive. 

Required probability = P(E) = [n(E)] / [n(S)] = 3 /16


An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known
P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15
Evaluate the following probabilities P(A fails|B has failed) ; P(A fails alone)

P(B fails) =P(A and B fail together ) + P(B fails alone) = 0.15+0.15 = 0.3

P(A fails|B has failed) = [P(A and B fail)] / [P(B fails ) ] = [0.15 / 0.30 =(1/2) = 0.5

P(A fails alone) = P(A fails) - P(A and B fail together ) = 0.2 – 0.15 = 0.05

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