Monochromatic Triangles
Six points are placed in general position and all 15 segments between pairs of them are drawn. Each segment is independently coloured red or blue with probability 1/2 each. A triangle (three of the points together with the three segments joining them) is monochromatic if its three segments all have the same colour. What is the expected number of monochromatic triangles? Give an exact number.
Related problems
Source: Classic indicator-variable exercise related to Ramsey theory; no single originator. Statement written for AxiomIQ.