MathDB

Bayus has eight slips of paper, which are labeled 1

, 2, 4, 8, 16, 32, 64,

and

128.

Uniformly at random, he draws three slips with replacement; suppose the three slips he draws are labeled

a, b,

and

c.

What is the probability that Bayus can form a quadratic polynomial with coefficients

a, b,

and

c,

in some order, with

2

distinct real roots?

Problem Statement