Derive Probabilities from Bayesian Network I have given the following Bayesian network.

I already know the fundamentals, for example, pairwise dependencies and how to calculate the total joint probability:
$$P(M,B,S,C,H) = P(M)\cdot P(S|M)\cdot P(B|M)\cdot P(C|S,B)\cdot P(H|B)$$
But now I want to calculate $P(M|S,C,H)$. I can easily apply Bayes Theorem to get:
$$P(M|S,C,H) = \frac{P(M,S,C,H)}{P(S,C,H)}$$
But I do not know how to calculate $P(M,S,C,H)$ and $P(S,C,H)$. I tried to solve it and got $P(M|S,C,H) = 0.5$. I strongly doubt that my calculations are correct because from sampling from the network with $1.000.000$ I got a relative frequency of about $0.2$.
EDIT: The sampling was performed incorrectly. It just proved that $P(M=1) = 0.2$. When performed correctly, it can be shown that the correct solution can be approximated with the sampled data from the network.

$$
\begin{align}
P(M=1|HCS=1)\overset{Bayes' law}= &\frac{P(HCS|M)\cdot P(M)}{P(HCS)}\\
 =& \frac{P(S|M) \cdot P(C|M) \cdot P(H|M) \cdot P(M)}{P(H) \cdot P(C) \cdot P(S)}\\
\text{with:}\\
P(S|M) =& 0.2\\
P(C|M) =& 0.8 \cdot 0.8 + 0.8 \cdot 0.2\\
P(H|M) =& 0.8 \cdot 0.8 + 0.6 \cdot 0.2\\
P(M) =& 0.2\\
\text{and:}\\
P(H) =& 0.8 \cdot 0.8 + 0.2 \cdot 0.6\\
P(C) =& 0.2 \cdot 0.8 \cdot 0.8 +\\
      & 0.8 \cdot 0.8 \cdot 0.8 +\\
      & 0.2 \cdot 0.2 \cdot 0.8 +\\
      & 0.8 \cdot 0.2 \cdot 0.05\\
P(S) =& 0.2 \cdot 0.2 + 0.8 \cdot 0.05
\end{align} 
$$
With that you get $P(M=1|HCS=1) \approx 0.588$.
