Let quad S =left{ M =left[ a _{ ij }right], a | vedclass

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Question

$M\left[\begin{array}{ll} a & b \ c & d \end{array}ight]$, where $a , b , c , d , \in\{0,1,2\}$

$n(s)=3^4=81$

we first bound $p (\ove

Vedclass · Accepted Answer

$\frac{50}{81}$

Vedclass · Answer

$M\left[\begin{array}{ll} a & b \ c & d \end{array}ight]$, where $a , b , c , d , \in\{0,1,2\}$

$n(s)=3^4=81$

we first bound $p (\overline{ A })$

$| m |=0 \Rightarrow ad = bc$

$ad = bc =0 \Rightarrow 	ext { no. of }(a, b, c, d)=\left(3^2-2^2ight)^2=25$

$ad = bc =1 \Rightarrow 	ext { no. of }( a , b , c , d )=1^2=1$

$ad = bc =2 \Rightarrow 	ext { no. of }( a , b , c , d )=2^2=4$

$ad = bc =4 \Rightarrow 	ext { no. of }( a , b , c , d )=1^2=1$

$: P (\overline{ A })=\frac{31}{81} \Rightarrow p ( A )=\frac{50}{81}$

Let $\quad S =\left\{ M =\left[ a _{ ij }\right], a _{ ij } \in\{0,1,2\}, 1 \leq i , j \leq 2\right\}$ be a sample space and $A=\{M \in S: M$ is invertible $\}$ be an event. Then $P ( A )$ is equal to

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