Consider the system of equations a x+b y=0, c x+d y=0, where a, b, c, d ∈ 0,1 STATEMENT - 1: The probability that the system of equations has a unique solution is 3 / 8. and STATEMENT -2: The probability that the system of equations has a solution is 1 .

Question

Consider the system of equations a x+b y=0, c x+d y=0, where a, b, c, d ∈ 0,1 STATEMENT - 1: The probability that the system of equations has a unique solution is 3 / 8. and STATEMENT -2: The probability that the system of equations has a solution is 1 . (A) Statement-1 is True, Statement -2 is True; Statement- 2 is a correct explanation for Statement-1 (B) Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement -1 is True, Statement -2 is False (D) Statement -1 is False, Statement -2 is True

Tardigrade Admin · Accepted Answer

For unique solution | a b c d | ≠ 0 where a , b , c , d ∈ 0,1 Total cases =16 Favorable cases =6 (Either ad =1, bc =0 or ad =0, bc =1) Probability that system of equations has unique solution is (6/16)=(3/8) and system of equations has either unique solution or infinite solutions so that probability for system to have a solution is 1 .

Q. Consider the system of equations ax+by=0,cx+dy=0, where a,b,c,d∈{0,1} STATEMENT - 1: The probability that the system of equations has a unique solution is 3/8. and STATEMENT -2 : The probability that the system of equations has a solution is 1 .

Statement-1 is True, Statement -2 is True; Statement- 2 is a correct explanation for Statement-1

Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement-1

Statement -1 is True, Statement -2 is False

Statement -1 is False, Statement -2 is True

Q. Consider the system of equations $a x + b y = 0, c x + d y = 0$ , where $a, b, c, d \in {0, 1}$
STATEMENT - 1: The probability that the system of equations has a unique solution is $3/8$ .
and
STATEMENT -2 : The probability that the system of equations has a solution is 1 .