question_answer 1)

If each element of a second order determinant is either zero or one, what is the probability that he value of the determinant is positive ? (Assume that the individual entries of the determinant are choosen independently, each value being assumed with probability  

Answer:

 Let the given determinant is             where (i)     If either of a11 of a22 is zero, then         Therefore, we must take                         ? (1) (ii)    If a12 = a21 = 1, then by (1)       If {a12 = 0 and a21 = 1}; {a12 =1 and a21 = 0}       and {a12 = a21 = 0}; then by (1)             (Probability of chosen of a11 = 1, a22 = 1,       a12 = 0, a21 = 1)        (Probability of chosen of a11 = 1, a22 = 1, a12= 1, a21 = 0)   (Probability of chosen of a11 = 1, a22 = 1, a12= 1, a21 = 0)               Required probability