I.

Choose B; EP=20.

II.

DF=ditch-fire; F=fire without ditch; UF=uncontrolled fire; CF=controlled fire; N=no fire

Choose DF; EP=42

III.

Test for oil=T; positive test return for oil=P; sell=S; drill=D; oil is present=O; market is good=G; market is average=A; market is bad=B.

First we need to obtain the inverse conditional probabilities by Bayes theorem.

Hence, rounding figures,

Pr(P)=.48;

Pr(O|P)= (.9x.3)/[(.3x.9)+(.7x.3)]=.56;

Pr(-O|-P)=(.7x.7)/[(.3x.1)+(.7x.7)]=.94.

We can now construct the decision tree.

You should not test and then you should drill; EP=+187.