Home
Class 12
MATHS
If each element of a second order determ...

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive?
(Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability `1/2`)

Text Solution

AI Generated Solution

To solve the problem, we need to find the probability that the determinant of a second-order matrix (2x2 matrix) with entries either 0 or 1 is positive. ### Step-by-Step Solution: 1. **Define the Determinant**: For a 2x2 matrix with elements \( a, b, c, d \), the determinant is given by: \[ \text{Determinant} = ad - bc ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If each element of a second order determinant is either zero or one,what is the probability that the value the determinant is non- negative?

A determinant of the second order is made with the elements 0 and 1. What is the probability that the determinant made is non-negative?

Knowledge Check

  • A determinant of second order of is made with the elements 0,1 . What is the probability that the determinant is positive?

    A
    `(7)/(12)`
    B
    `(11)/(12)`
    C
    `(3)/(16)`
    D
    `(15)/(16)`
  • If each element of a determinant of third order with value A is multiplied by 3, then the value of newly formed determinant is

    A
    3A
    B
    9A
    C
    27A
    D
    none of these
  • A determinant of second order is made with elements 0 and 1. The probability that the determinant made is non-negative is equal to

    A
    `(11)/(16)`
    B
    `(13)/(16)`
    C
    `(9)/(16)`
    D
    `(7)/(16)`
  • Similar Questions

    Explore conceptually related problems

    Minimum value of a second order determinant whose each is either 1 or 2 is equal to

    If the entries in a 3xx3 determinant are either 0 or 1, then the greatest value of their determinants is

    Find the value of the determinant: |(4,-2),(3,1)|

    Minimum value of a second order determinant whose each entry is either 1or 2is equal to

    If every element of a third order determinant of value Detlta is multiplied by 5, then the value of new determinant, is