Homework SourseChoose independently two numbers B and C at random from the
Choose independently two numbers B and C at random from the interval [-1,1] with uniform distribution, and consider the quadratic equation x^2 + Bx 4- C = 0 . Find the probability that the roots of this equation are both real.![Choose independently two numbers B and C at random from the interval [-1,1] with uniform distribution, and consider the quadratic equation x^2 + Bx 4- C = 0 .](/WebImages/4/choose-independently-two-numbers-b-and-c-at-random-from-the-977703-1761501650-0.webp "Choose independently two numbers B and C at random from the interval [-1,1] with uniform distribution, and consider the quadratic equation x^2 + Bx 4- C = 0 .")
Solution
Here we are to find P(B2-4C>0)=P(B2>4C)=P(B2>4C,C>0)+P(B2>4C,C<0)=0.5+P(B2>4C,C>0)=0.5+1/24=13/24
