Probability, Probability Theory, Philosophy Of Mathematics.
P(HH) = XY, and similarly P(TT) = (1-X)(1-Y). Therefore, P(HH ⋃ TT) = XY + (1-X)(1-Y) = 0.5. Then, solve for Y → 2XY — X — Y + 1 = 0.5 → 2XY — Y = X — 0.5 → Y(2X-1) = X — 0.5 → Y = X-0.5 / 2X-1. By inspection, the numerator is half of the denominator. so Y = 0.5. (2) Or the simple answer is just to