Given an $n \times n$ matrix filled with random variables with distribution $a$, how to calculate the probability of positive-definitness of this matrix if $a \sim N(0,1)$ and the matrix is symmetric?

Given an $n \times n$ symmetric random matrix whose entries have distribution $N(0,1)$, how to calculate the probability of positive definiteness of this matrix?

Given an $n \times n$ matrix filled with random variables with distribution $a$, how to calculate the probability of positive-definitness of this matrix if $a \sim N(0,1)$ and the matrix is (respectively is not) symmetric?

Given an $n \times n$ matrix filled with random variables with distribution $a$, how to calculate the probability of positive-definitness of this matrix if $a \sim N(0,1)$ and the matrix is symmetric?

Given nxn matrix, that builded by random variables with distribution N(0,1). How to calculate probability of positive-definitness of this matrix if:

1. matrix is symmetric
2. matrix is not symmetric

Given an $n \times n$ matrix filled with random variables with distribution $a$, how to calculate the probability of positive-definitness of this matrix if $a \sim N(0,1)$ and the matrix is (respectively is not) symmetric?