【摘要】 作者在本文中討論条件概率、一般概率与复合概率的計算方法,并且指出M.Wurtele計算各种风向时候雾的概率,所用的方法是不必要的。作者也計算了各种风向时的降水概率,并且根据总概率定理計算降水的一般概率,根据Bayes定理計算在降水出現的条件下风的概率. 其次,作者推导計算各台站同时为雨日的概率,并且推导校对公式,以便检查計算結果。更多还原

【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\W_i）=P（W_iF）/P（W_i） （1） where F represents the fog frequency and W_i 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.The conditional probabilities of rainfall for the different wind directions have been calculated also by the same method as stated above. Furthermore, the attempts have been made to calculate the general probability of rainfall by applying the theorem of total probability and to calculate the conditional probability of wind direction after the rainfall has been observed by applying Bayes’ theorem.In the second part it has been shown that P（B）=P（B₀）+P（B₁）+…+P（B_n）, （2） where B denotes the event of having rain days at the station B; B₀ denotes the event of having rain days only at the station B; B₁ denotes the event that two stations including station B have rain days; B₂ denotes the event that three stations including the station B have rain days; and so on. Besides, by the theorem of compound probability the following formulas can be established: where i=1, 2,…n; i, j are taken for all combinations in the numbers 1, 2,…n; k=1, 2,…n except the numbers i and j; A₀=1.By formula （3） the probabilities of simultaneous occurrence of rain days at Hankow, Siangyang, Changsha and Chungking have been calculated for the different months. For the purpose of check the following three formulas have been derived in addition to the formula （2）:P（B）=P（B₀）+2/3 P（B₁）+1/3 P（B₂）+1/3 [P（BA₁）+P（BA₂）+P（BA₃）], （4）P（BA₁）+P（BA₂）+P（BA₃）=P（B₁）+3/2 P（B₂）+3/2 P（B₃）+1/2 [P（BA₁A₂）++P（BA₂A₃）+P（BA₁A₃）] （5）andP（BA₁A₂）+P（BA₂A₃）+P（BA₁A₂）=P（B₂）+3P（B₃）. （6）At last the author has demonstrated that the computation of the compound probability by formula （3） is more significant than that by direct computation from the definition of probability.更多还原