Eidetic Geometry

@quant.bsky.social

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(huge dipshit voice)

Picture of the sun
A & = \{\text{correct in first 3 guesses}\} \\ B & = \{\text{correct on 4th guess}\} \\ X & = \text{the partition containing the answer after 3 guesses} \\ & \qquad \text{taking values in } x_{1}, x_{2}, \dots, x_{8} \\ ~ \\ P(\text{correct}) & = P(A) + P(B) \\ & = \frac{7}{35} + P(B) \\ & = \frac{7}{35} + E(P(B|X)) \\ & = \frac{7}{35} + \sum_{i=1}^{8}P(B|X=x_{i})P(X=x_{i}) \\ & = \frac{7}{35} + \sum_{i=1}^{8}\frac{1}{|x_{i}|}\frac{|x_{i}|}{35} \\ & = \frac{7}{35} + \frac{8}{35} \\ & = \frac{3}{7}