GATE 2024 DA – Question 64

Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables:

[Figure: a network with $U$ pointing to $V$ and $W$, and $V$ and $W$ both pointing to $Z$. $P(U = 0) = P(U = 1) = 0.5$. $P(V|U)$ is 0.5 and 0.5 for both values of $U$. $W$ copies $U$: $P(W = 1|U = 1) = 1$ and $P(W = 0|U = 0) = 1$. $P(Z = 1|V, W)$ is 0.5 for $(V, W) = (0, 0)$, 0 for $(0, 1)$, 0 for $(1, 0)$ and 0.5 for $(1, 1)$.]

The value of $P(U = 1, V = 1, W = 1, Z = 1) = $ ______ (rounded off to three decimal places).