(c) 7/16
x2 + ax + b = 0 ⇒ \(x = {-a \pm \sqrt{a^2-4b} \over 2}\)
Given that the roots are real ⇒ a2 – 4b ≥ 0 or a2 > 4b
When a = 1, b = 1 or 2 or 3 or 4, a2 – 4b < 0
When a = 2, b = 1, a2 – 4b = 0
When a = 3, b = 1 or 2 for which a2 – 4b ≥ 0
When a = 4, b = 1 or 2, 3 or 4 for which a2 – 4b ≥ 0
So, Selecting from the 4 number 42 = 16 ways.
(i.e.,) n(s) = 16
n(A) = (2 or 3 or 4) = 3
n(B) = (1 or 2 or 3 or 4) = 4
P(A) + P(B) = 3/16 + 4/16 = 7/16