Introduction to Probability · Problem 2.2.14

Combinatorics — Grinstead & Snell

Mathematics — Probability · continuous-density-functions

Problem

Choose independently two numbers BB and CC at random from the interval [−1,1][-1, 1] with uniform distribution, and consider the quadratic equation x2+Bx+C=0.x^2 + Bx + C = 0. Find the probability that the roots of this equation (a) are both real. (b) are both positive. Hints: (a) requires 0≤B2−4C0 \leq B^2 - 4C, (b) requires 0≤B2−4C0 \leq B^2 - 4C, B≤0B \leq 0, 0≤C0 \leq C.

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