WBJEE · Maths · Probability
A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is
- A \(\frac{3}{16}\)
- B \(\frac{3}{8}\)
- C \(\frac{1}{4}\)
- D \(\frac{5}{8}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{8}\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ll}a & b \\ c & d\end{array}\right|=a d-b c=0\) Case \(1: a d=b c=0 \rightarrow 3 \times 3=9\) cases Case \(2:\) ad \(=\mathrm{bc}=1 \rightarrow 1\) case only \(\therefore\) Probability \(=1-\frac{9+1}{2^4}=\frac{3}{8}\)
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