The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :

Question

The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to : (A) (133/104) (B) (18/103) (C) (19/103) (D) (271/104)

Tardigrade Admin · Accepted Answer

Let matrix A is singular then | A |=0 Number of singular matrix = All entries are same + only two prime number are used in matrix =10+10 × 9 × 2 =190 Required probability =(190/104)=(19/103)

Q. The probability that a randomly chosen $2 \times 2$ matrix with all the entries from the set of first $10$ primes, is singular, is equal to :

$\frac{133}{1 0 ^{4}}$

$\frac{18}{1 0 ^{3}}$

$\frac{19}{1 0 ^{3}}$

$\frac{271}{1 0 ^{4}}$

Let matrix $A$ is singular then $∣ A ∣ = 0$
Number of singular matrix $=$ All entries are same $+$ only two prime number are used in matrix
$= 10 + 10 \times 9 \times 2$
$= 190$
Required probability $= \frac{190}{1 0 ^{4}} = \frac{19}{1 0 ^{3}}$

Q. The probability that a randomly chosen 2×2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :

104133​

10318​

10319​

104271​