Abstract: The author first discussed the evaluation of the conditional probability and the general probability, and then discussed the evaluation of the compound probability. The first part of this paper deals with the conditional probabilities of fog for the different wind directions and shows that it is better calculated by the equation:P(F|Wi)=P(WiF)/P(Wi)(1) where F represents the fog frequency and Wi represents the frequency of the wind from the direction i(i=1, 2,…16). By practical calculations it shows that the method adopted by M. Wurtele(1944) was unnecessary.