A determinant of second order is made with the elements 0, 1. What is

1.	A determinant of second order is made with the elements 0, 1. What is the probability that the determinant is positive?(a) \(\frac{7}{12}\)(b) \(\frac{11}{12}\)(c) \(\frac{3}{16}\)(d) \(\frac{15}{16}\)
Answer» (c) \(\frac{3}{16}\) Total number of determinants that can be formed using 0 and 1 = 16 (4 × 4) The positive determinants are \(\begin{bmatrix}1&0\\[0.3em]1&1\end{bmatrix}\),\(\begin{bmatrix}1&0\\[0.3em]0&1\end{bmatrix}\),\(\begin{bmatrix}1&1\\[0.3em]0&1\end{bmatrix}\), i.e, 3 in number. ∴ Required probability = \(\frac{3}{16}.\)

A determinant of second order is made with the elements 0, 1. What is the probability that the determinant is positive?(a) \(\frac{7}{12}\)(b) \(\frac{11}{12}\)(c) \(\frac{3}{16}\)(d) \(\frac{15}{16}\)

Answer»

(c) \(\frac{3}{16}\)

Total number of determinants that can be formed using 0 and 1 = 16 (4 × 4)

The positive determinants are \(\begin{bmatrix}1&0\\[0.3em]1&1\end{bmatrix}\),\(\begin{bmatrix}1&0\\[0.3em]0&1\end{bmatrix}\),\(\begin{bmatrix}1&1\\[0.3em]0&1\end{bmatrix}\), i.e, 3 in number.

∴ Required probability = \(\frac{3}{16}.\)

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A determinant of second order is made with the elements 0, 1. What is the probability that the determinant is positive?(a) \(\frac{7}{12}\)(b) \(\frac{11}{12}\)(c) \(\frac{3}{16}\)(d) \(\frac{15}{16}\)

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