Question

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? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability \(\frac{1}{2}\)).

Answer 1

iven that a second order determinant has 4 entries, which may be 0 or 1. Total number of determinants = 24=16
We need to find the probability that the determinant is positive.
The only positive determinants are | 1 0 0 1 |,| 1 1 0 1 |and| 1 0 1 1 |
Therefore the required probability =
3
16

i hope this helps

Answer 2

Answer:

$= \frac{3}{16}$

Step-by-step explanation:

There are four entries in determinant of 2 × 2 order.

Each entry may be filled up in two ways with 0 or 1.

Therefore, number of determinant that can be formed 2⁴ = 16

The value of determinant is +ve in the following cases.

$\left[\begin{array}{ccc}0&1\\0&1\\\end{array}\right]$

$\left[\begin{array}{ccc}1&0\\1&1\\\end{array}\right]$

$\left[\begin{array}{ccc}1&1\\0&1\\\end{array}\right]$

          3 determinants.

Thus, the probability that the determinant is positive = $\frac{3}{16}$

GOOD LUCK !!