For equal roots discriminant D=0⇒b2−16c=0. b2=4×4×c ⇒c has to be perfect square. Then, c can be any perfect square numbers from the given sets and the perfect square number in the set S =1,4,9,16,25,36,49,64,81,100 ∴ Number of ordered pair (b,c) will be 10 ∴ Required probability =