A determinant of the second order is made with elements 0 and 1 . What is the probability that the determinant made is non-negative?

Step-by-step solution

A second order determinant is given by vmatrix a & b c & d vmatrix = ad - bc . Each element a, b, c, d can take values from the set 0, 1 . Since there are 4 positions and each position has 2 choices, the total number of possible determinants is 2^4 = 16 . We want to find the number of cases where ad - bc 0 , which is equivalent to ad bc . Let us list the possible values of ad and bc : If ad = 1 , then a=1 and d=1 (1 case). If ad = 0 , then (a,d) (0,0), (0,1), (1,0) (3 cases). Similarly, bc = 1 occurs in 1 case and