11. Quadractic Quizzicality
Question: Suppose B and C are random numbers from a uniform(0,1) distribution. What is the probabilty that x^2 + Bx + C = 0 has two real roots?
Solution: x has two real roots if its discriminant is greater than zero. i.e B^2 - 4C > 0.
So B^2 > 4C or c < B^2/4.
The sample space for B and C has an area of 1 and the area beneath the curve of C = B^2/4 represents the values for B and C that result in real roots.
So the probabilty that B^2 - 4C > 0 (the equation x^2 + Bx + C = 0 has two real roots) is the integral from 0 to 1 of B^2 /4 which is 1/12.