# Probability of a matrix having determinant zero

What would be the probability of matrix having determinant zero out of all matrices with all entries being positive? How does one calculate such?

Edit: Restriction to natural numbers and size of $n \times n$. Restriction to entries from 0 to 5 or from 0 to 10.

• How are the entries chosen? If from the reals with independent uniforms on $[0,1]$ say, the probability is $0$. Indeed the answer is $0$ for any independent random variables with any continuous distribution. Dec 10, 2012 at 7:30
• You can't answer this question unless you know what the distribution is. Dec 10, 2012 at 7:30
• Even with your edit, you still can't answer it unless you know the probability that each number occurs. Dec 10, 2012 at 7:36
• After my edit, is this answerable? Oh.. but then distribution... OK, I will provide distribution.
– DDR
Dec 10, 2012 at 7:39
• The distribution(s) you chose seem(s) to eliminate all hope of an underlying structure to the problem.
– Did
Dec 10, 2012 at 7:51