Question: [40 points]

Let A, B and C be independent random variables with the following distributions:

P(A = 1) = 0.4, P(A = 2) = 0.6

P(B = -3) = 0.25, P(B = -2) = 0.25, P(B = -1) = 0.25, P(B = 1) = 0.25

P(C = 1) = 0.5, P(C = 2) = 0.4, P(C = 3) = 0.1

1. [20 points] What is the probability that the quadratic equation
   \[A{{x}^{2}}+Bx+C=0\]
   has two real roots that are different?
2. [20 points] What is the probability that the quadratic equation

has two real roots that are both strictly positive?

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Deliverable: Word Document