If each element of a second order determinant is either zero or one, the probability that the value of determinant is non-positive is
An element in probability refers to a single outcome within a sample space of a random experiment. Each element represents a possible result and helps in defining events. The total number of elements in a sample space determines probability calculations which are essential for analyzing uncertainty and making informed decisions in real-life situations.
Class 12 Maths Probability is explained in Chapter 13 for the CBSE Exam 2024-25. It covers important concepts like sample space random experiments independent and dependent events mutually exclusive and non-mutually exclusive events Bayes’ theorem and conditional probability. These topics help in solving real-life problems and are useful for higher studies and competitive exams.
Share
A second-order determinant is of the form:
| a b |
| c d |
Each element (a, b, c, d) can be either 0 or 1.
Total possible cases = 2⁴ = 16
The determinant value is given by:
Det = (a × d) – (b × c)
For the determinant to be **non-positive**, we need:
(a × d) – (b × c) ≤ 0
Now, let’s count the favorable cases:
1. Cases where determinant = 0:
– (a, b, c, d) = (0,0,0,0) → Det = (0×0) – (0×0) = 0
– (0,0,0,1) → (0×1) – (0×0) = 0
– (0,0,1,0) → (0×0) – (0×1) = 0
– (0,1,0,0) → (0×0) – (1×0) = 0
– (1,0,0,0) → (1×0) – (0×0) = 0
– (1,1,1,1) → (1×1) – (1×1) = 0
So, 6 cases where Det = 0.
2. Cases where determinant < 0:
– (0,1,1,0) → (0×0) – (1×1) = -1
– (1,1,0,0) → (1×0) – (1×0) = 0
– (0,0,1,1) → (0×1) – (0×1) = 0
– (1,0,0,1) → (1×1) – (0×0) = 1 (not negative)
So, 5 cases where Det < 0.
Total favorable cases = 6 (Det = 0) + 5 (Det < 0) = 11
Probability = 11/16
Click here for more:
https://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-13