JEE Advanced 2008 Paper 1Question 1
Consider the system of equations $ax+by=0$, $cx+dy=0$, where $a,b,c,d\in\{0,1\}$.
STATEMENT-1: The probability that the system of equations has a unique solution is $\frac38$.
and
STATEMENT-2: The probability that the system of equations has a solution is 1.
Probability
Solution
Unique solution iff $ad-bc\ne0$: with entries in $\{0,1\}$ there are 6 such matrices out of 16, so $P=\frac38$ (True). A homogeneous system always has the solution $x=y=0$, so Statement-2 is True, but it does not explain the $\frac38$.