JEE Mains · Maths · STD 11 - 14. probability
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
- A \(\frac{50}{81}\)
- B \(\frac{47}{81}\)
- C \(\frac{49}{81}\)
- D \(\frac{16}{27}\)
Answer & Solution
Correct Answer
(A) \(\frac{50}{81}\)
Step-by-step Solution
Detailed explanation
\(M\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]\), where \(a , b , c , d , \in\{0,1,2\}\) \(n(s)=3^4=81\) we first bound \(p (\overline{ A })\) \(| m |=0 \Rightarrow ad = bc\) \(ad = bc =0 \Rightarrow \text { no. of }(a, b, c, d)=\left(3^2-2^2\right)^2=25\)…
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