Problem 14
On February 2nd, groundhogs all across the country awake from a long winter sleep to look for their shadows. If a groundhog in a given area sees his shadow, he decides that another six weeks of winter must be on its way, and he returns to his hole. If the groundhog does not see his shadow, he concludes that spring must be near, so he stays above ground.
Looking at the statistics from 2003, it was found that when a longer winter occurred in a given area, the groundhog in that area had a 99 percent chance of seeing his shadow (wow! those groundhogs make great meteorologists). However, in areas that had shorter winters, groundhogs still had a 17 percent chance of seeing their shadows which led to incorrect predictions about the length of the winter ahead. It is also known that 25 percent of the areas tested by groundhogs last year had longer winters. So, if a groundhog in a certain area saw his shadow last year and retreated to his hole, what is the probability that a long winter was actually on its way?
