GATE DA 2024 Q64: Joint probability from a Bayesian network's tables

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

The network has edges $U \to V$ , $U \to W$ , $V \to Z$ and $W \to Z$ .

	$P(\cdot)$
$U = 0$	0.5
$U = 1$	0.5

	$P(V = 0 \mid \cdot)$	$P(V = 1 \mid \cdot)$
$U = 0$	0.5	0.5
$U = 1$	0.5	0.5

	$P(W = 0 \mid \cdot)$	$P(W = 1 \mid \cdot)$
$U = 0$	1	0
$U = 1$	0	1

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

Try it: numerical answer: type the value

Your answer

Numerical answer. No negative marking.

Show answer and explanation

Answer: 0.125 (official GATE 2024 final answer key)

Concept used: A Bayesian network's joint probability is the product of each variable's probability given its parents.

First step: $P(U{=}1)\,P(V{=}1 \mid U{=}1)\,P(W{=}1 \mid U{=}1)\,P(Z{=}1 \mid V{=}1, W{=}1) = 0.5 \times 0.5 \times 1 \times 0.5$ .

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key