Wednesday, October 21, 2009

[数学]连续两天降雨的概率

问题:(from mitbbs) Weather forecast: 50% chance of rain tomorrow, 75% chance of rain the day after tomorrow. What is the chance of rain for both tomorrow and the day after tomorrow?

Sol: 50%*75%? 这并不是一个严谨的答案.因为明天降雨和后天降雨未必是两个独立事件. 所以应该给出的是一个界

1/4=max{0, P[明天降雨]+ P[后天降雨]-1}< P[明天降雨 and 后天降雨] < min{P[明天降雨], P[后天降雨]}=1/2

No comments: