Let Ax2 Bx C 0 are real 03 respectively What is the proba

Let Ax^2 + Bx + C = 0 are real? [0,3] respectively. What is the probability that both roots of the equation [0,1], and [0,2 ], C be independent random variables, uniformly distributed over B , and A ,

Solution

For the equation to have roots real discriminant >0

i.e. B^2 -4Ac>0

Or B^2 >= 4AC

A <= 1/2 and B <=1/2

Prob(B^2>=4ac) = P(A<=1/2 and C<=1/2)

= 0.25+0.1667 = 0.4167