Question
Question: A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 o...
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
A
3/16
B
3/8
C
¼
D
None of these
Answer
3/8
Explanation
Solution
A determinant of order 2 is of the form A = 
.
It is equal to ad-bc. The total number of ways of choosing a, b, c and d is 2x2x2x2=16. Now ∆ ≠0 if and only if either ad = 1, bc = 0 or ad = 0, bc = 1. But ad = 1, bc = 0 iff a = d = 1 and one of b, c is zero. Therefore ad = 1, bc = 0 in three cases, similarly ad = 0, bc = 1 in three cases. Therefore the required probability = 6/16 = 3/8.