Thank you for reporting, we will resolve it shortly
Q.
A second order determinant is written randomly using the numbers 1 and - 1 as its elements, the probability that the value of the determinant is non zero, is
Probability
Solution:
$n\left(S\right) = 2^{4} = 16$
($\because$ There are four places to fill with 1 and -1 i.e., every place can be filled by 2 ways).
$n\left(A\right) =$ Number of determinants whose value is zero
$\therefore n\left(A\right) =$ It can be happened if all entry are +ve = 1 case
only two entries are negative $ = \,{}^{4}C_{2} = 6$ cases
all four entries are negative $= \,{}^{4}C_{4} = 1$ case
$n\left(A\right) = 8$ like cases
$\therefore P\left(A\right) = \frac{n\left(A\right)}{n\left(S\right)} =\frac{8}{16} = \frac{1}{2}$
