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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