Problem $3.$

Mr$.$ Musk has recently visited Mars. Find the following probabilities:

a$)$ He will have a headache and no common cold.

b$)$ He will have a spontaneous combustion.

c$)$ He will have a runny nose but no headache.

The Bayesian Network and the conditional tables for this problem are given in figure $1.$

Assuming all six variables are binary, with $1$ representing "true" and $0$ "false", the probability tables for the network might be defined as follows:

$\backslash$table$[[P(V),P(C),P(F|V),P(R|C,F),P(H|C,F),P(S|F)$