Each year, on Groundhog's Day, February 2nd, everyone awaits the appearance of the groundhog.As the story has it, if he emerges from his hole and if it is sunny, he will be startled by his own shadow and quickly retreat back into his hole.This signals six more weeks of winter.However, if it is a cloudy day and he sees no shadow, spring-like weather will come early. There is a 25% chance that the groundhog will see his shadow on February 2.The probability of spring coming early if the groundhog sees his shadow is 20%; the probability of spring coming early if the groundhog does not see his shadow is 60%.Suppose that spring comes early this year.What is the probability that the groundhog saw his shadow on February 2?
A)50%
B)12%
C)10%
D)5%
E)2%

Question

Quizplus · Accepted Answer

Using Bayes' theorem, the probability that the groundhog saw his shadow given that spring comes early is calculated as follows: P(Shadow|Spring Early) = [P(Spring Early|Shadow) * P(Shadow)] / P(Spring Early). This results in (0.20 * 0.25) / [(0.20 * 0.25) + (0.60 * 0.75)] = 0.10 or 10%.

Each Year, on Groundhog's Day, February 2nd, Everyone Awaits the Appearance