Question

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 :

• A. $\frac{133}{10^{4}}$
• B. $\frac{18}{10^{3}}$
• C. $\frac{19}{10^{3}}$
• D. $\frac{271}{10^{4}}$

Answer 1

Answer: (C)

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 $=\frac{190}{10^{4}}=\frac{19}{10^{3}}$