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If each element of a second order determinant is either 0 or 1, what is the probability that the value of determinant is positive ? (Assume that the individual entries of the determinant are chosen independently, each value assumed with probability 1/2.

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There are four entries determinant of 2 x 2 order. Each entry may be filled up in two ways with 0 or 1. Therefore, number of determinant that can be formed = 24 = 16

The value of  determinant is positive in the following cases 

Thus, the probability that the determinants is positive = 3/16.

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