Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equationsx + y + z = 5x + 2y + 3z = $\mu$ x + 3y + $\lambda$z = 1is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :

Question

Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equations

x + y + z = 5

x + 2y + 3z = $\mu$

x + 3y + $\lambda$z = 1

is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :

$p = {1 \over 6}$ and $q = {1 \over 36}$

$p = {5 \over 6}$ and $q = {5 \over 36}$

$p = {5 \over 6}$ and $q = {1 \over 36}$

$p = {1 \over 6}$ and $q = {5 \over 36}$

Solution

Please login to view the detailed solution steps...

Go to DASH