A determinant is chosen at random from the se | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) determinant of order $2$ is of the form $\Delta = \begin{vmatrix} a & b \ c & d \end{vmatrix} = ad - bc$.Each element $a, b, c, d$ can be chosen

Vedclass · Accepted Answer

$\frac{3}{8}$

Vedclass · Answer

(B) determinant of order $2$ is of the form $\Delta = \begin{vmatrix} a & b \ c & d \end{vmatrix} = ad - bc$.Each element $a, b, c, d$ can be chosen in $2$ ways ($0$ or $1$).Total number of possible determinants = $2^4 = 16$.The determinant $\Delta$ is non-zero if $ad - bc 
eq 0$,which means $ad 
eq bc$.Since $a, b, c, d \in \{0, 1\}$,the possible values for $ad$ and $bc$ are $0$ or $1$.$ad - bc = 0$ occurs when $ad = bc$. This happens in the following cases:$1$. $ad = 0$ and $bc = 0$: $ad=0$ occurs in $3$ ways $((0,0), (0,1), (1,0))$,and $bc=0$ occurs in $3$ ways. Total ways = $3 	imes 3 = 9$.$2$. $ad = 1$ and $bc = 1$: $ad=1$ occurs in $1$ way $((1,1))$,and $bc=1$ occurs in $1$ way. Total ways = $1 	imes 1 = 1$.Total cases where $\Delta = 0$ is $9 + 1 = 10$.Total cases where $\Delta 
eq 0$ is $16 - 10 = 6$.Therefore,the required probability = $\frac{6}{16} = \frac{3}{8}$.

$A$ 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

Similar Questions

$A$ bag contains $3$ white,$3$ black,and $2$ red balls. Three balls are drawn one by one without replacement. The probability that the third ball is red is:

If $A$ and $B$ are two independent events,then $A$ and $\bar B$ are

$2$ dice are thrown together. What is the probability that the sum of the numbers on $2$ faces is neither $9$ nor $11$?

If the events $A$ and $B$ are mutually exclusive,then $P\left( \frac{A}{B} \right) = $

$A$ card is drawn randomly from a pack of playing cards. The probability that it is neither an ace nor a king is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module