We know, given the nature of the problem that $Y = H \vee (X \land B)$ This can be reframed as a more concrete counterfactual : $PS_{01} = P(Y_1 = 1 | Y_0 = 0 )$ Where $Y_1$ is the event $H \land B$ and $Y_0$ is the event $H$. $PS_{01}$ is the probability that a death is caused by Russian Roulette alone. Now let, $PS_{10} = P(Y_1 = 0 | Y_0 = 1 )$ By definition, since $Y_1$ contains $Y_0$, $PS_{10} = 0$ The law of total probability gives us : $P(Y_1 = 1) = (1 - PS_{10})(P(Y_0 = 1)) + PS_{01}(1 - P(Y_0 = 1))$ We can then solve for $PS_{01}$ to get : $\frac{P(Y_1 = 1) + P(Y_0 = 1)}{1 - P(Y_0 = 1)} = \frac{1}{6}$ Now we use the equation derived from the law of total probability and plug in values for NYC, to get the estimated mortality rate as $20.8%$

Thus using the structural diagram(s) and functional constraints, we've managed to solve this problem using only the two assumptions we began with.