Question

Choose the correct answer :

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

Answer 1

Answer: (C)

$\frac{19}{10^3}$

Answer 2

The correct option is(C): $\frac{19}{10^3}$

Let A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

Let E be the event that matrix of order 2 × 2 is singular

$P[E]=\frac{C_1^{10}+C_2^{10}×2×2}{10^4}=\frac{190}{10^4}=\frac{19}{10^3}$