1 pt Let A B and C be independent random variables uniformly

(1 pt) Let A, B, and C be independent random variables, uniformly distributed over [0,2], [0, 10], and [0,6] respectively. What ?s the probability that both roots of the equation Ax2 + Bx + C = O are real?

Solution

if the quadratic equation has real roots then discriminant >=0

i.e. B²-4AC>=0

A has pdf = 0.5, B has 0.1 and C has 0.6

4ac varies from 0 to 48

while b^2 varies from 0 to 100

For b^2 to be less than 48 has probability = 47.9999/100 = 0.4799

For real roots probability = b^2 taking value 48 to 100

= 0.52