 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says if each element of a second order determinant is either 0 or 1, 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 probability 1 over 2. So, let's start the solution. According to the given question, each element of a second order determinant is either 0 or 1. Now the determinant of order 2 by 2 is a11, a12, a21, a22 and this is equal to a11 into a22 minus a21 into a12. Each element of this determinant is either 0 or 1. Now the number of determinants that can be formed by using the digits 0 or 1 is equal to 2 raised to power 4. This is equal to 16. Now we have to find what is the probability that the value of the determinant is positive? So, the value of the determinant is positive a11 into a22 minus a21 into a12 is greater than 0. That is a11 into a22 is greater than a21 into a12 since each element of the given determinant is either 0 or 1. So, this is possible only if a11 is equal to a22 is equal to 1. One of the elements or both the elements a21, a12 are 0. Hence, the all possible determinants are 1100. That is here a11 is equal to a22 is equal to 1 and both the elements a21 and a12 are 0. Similarly, we have 11 and there in this determinant a21 is 1 and a12 is 0. Again, we can have the determinant of the form 1101. Hence, the probability that the value of the determinant is positive is equal to 3 over 16. So, the answer for the above question is 3 over 16. So, this completes our session. I hope the solution is clear to you. Bye and have a nice day.