If each element of a second order determinant is zero or one , what is the probability that the values of the determinant is positive?(Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability12
A second order determinant has four entries which may be 0 or 1.
Total number of determinants=2=16
The only positive determinants are ∣∣∣1001∣∣∣∣∣∣1011∣∣∣and∣∣∣1101∣∣∣.
Since, each entry of the above determinant can be selected with probability 12 , therefore required probability.
=3(12×12×12×12)=316.
Alternatively Here, total number of cases=16
Favourable number of cases=3
∴Required probability=316