Question:
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? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability1/2 ).
Answer:
Given that each element of a second order determinant is either 0 or 1.
So total number of determinants of second order with each element with 0 and 1 = 24 = 16
The value of determinant is positive in 3 cases i.e.
|1 0| |1 1| |1 0|
|0 1| |0 1| |1 1|
So required probability= 3/16
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