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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 value of the determinant chosen is positive is
- a)1/4
- b)1/16
- c)2/16
- d)3/16
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A determinant is chosen at random from the set of all determinants of ...
Total number of determinant =2 ^ 4 =16
The positive determinants are [1 1 0 1 ], [1 0 1 1], [1 0 0 1]
Therefore required probability = 3/16
Most Upvoted Answer
A determinant is chosen at random from the set of all determinants of ...
Solution:
We know that the determinant of a 2x2 matrix is given by:
$$\begin{vmatrix}
a & b\\
c & d
\end{vmatrix} = ad - bc$$
a & b\\
c & d
\end{vmatrix} = ad - bc$$
As the determinant can only take values of 0 or 1, the possible matrices are:
$$\begin{vmatrix}
0 & 0\\
0 & 0
\end{vmatrix} = 0$$
0 & 0\\
0 & 0
\end{vmatrix} = 0$$
$$\begin{vmatrix}
0 & 1\\
0 & 0
\end{vmatrix} = 0$$
0 & 1\\
0 & 0
\end{vmatrix} = 0$$
$$\begin{vmatrix}
1 & 0\\
0 & 0
\end{vmatrix} = 0$$
1 & 0\\
0 & 0
\end{vmatrix} = 0$$
$$\begin{vmatrix}
1 & 1\\
0 & 0
\end{vmatrix} = 0$$
1 & 1\\
0 & 0
\end{vmatrix} = 0$$
$$\begin{vmatrix}
0 & 0\\
1 & 1
\end{vmatrix} = 0$$
0 & 0\\
1 & 1
\end{vmatrix} = 0$$
$$\begin{vmatrix}
0 & 1\\
1 & 0
\end{vmatrix} = -1$$
0 & 1\\
1 & 0
\end{vmatrix} = -1$$
$$\begin{vmatrix}
1 & 0\\
0 & 1
\end{vmatrix} = 1$$
1 & 0\\
0 & 1
\end{vmatrix} = 1$$
$$\begin{vmatrix}
1 & 1\\
1 & 1
\end{vmatrix} = 0$$
1 & 1\\
1 & 1
\end{vmatrix} = 0$$
Out of the 8 possible matrices, only 2 have a positive determinant. Therefore, the probability of choosing a matrix with a positive determinant is:
$$\frac{2}{8} = \frac{1}{4} = 0.25$$
Therefore, the correct option is (d) 3/16.
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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 value of the determinant chosen is positive isa)1/4b)1/16c)2/16d)3/16Correct answer is option 'D'. Can you explain this answer?
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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 value of the determinant chosen is positive isa)1/4b)1/16c)2/16d)3/16Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 value of the determinant chosen is positive isa)1/4b)1/16c)2/16d)3/16Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 value of the determinant chosen is positive isa)1/4b)1/16c)2/16d)3/16Correct answer is option 'D'. Can you explain this answer?.
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