If a 1 ,   a 2 ,   b 1 and b 2 take values in the set 1 , - 1,0 , then the probability that the equation a 1 a 2 = b 1 b 2 is satisfied is p q , ( p & q are co-prime) then, q - 2 p is

Step-by-step solution

Total ways is 3 4 Now, a 1 a 2 = b 1 b 2 If, Case 1 a 1 a 2 = b 1 b 2 = 0 If at least one of a 1   o r   a 2 and b 1   o r   b 2 is “ 0 ” i.e. 3 2 - 2 2 ways Case 2 a 1 a 2 = b 1 b 2 = + 1 Both a 1 , a 2   is   + 1 or – 1 i.e. 2 2 ways Case 3 a 1 a 2 = b 1 b 2 = - 1 2 2 ways Hence, required probability = 3 2 - 2 2 + 4 + 4 3 4 = 33 81 = 11 27