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? (Assuming that the individual entries of eth determinant are chosen independently, each value being assumed with probability 1/2).

Answer

N/a

Explanation

Let a determinant of order 2 whose number of elements are 4, have all elements eitther 0 or 1.
Total number of determinants `=2^(4)=16`
In which the positive determinants are
`|(1, 0),(0,1)|,|(1, 0),(1, 1)|` and `|(1 ,1),(0, 1)|`
Since the probability of selecting each of above determinant is `1/16`.
Therefore, required probability `=3/16`