You just bought a big bag of 200 candies for handing out on Hallowe’en. Unfortunately, you have somewhat of a sweet tooth, and you raid the bag twice per day, each time taking from three to five candies.

What is the probability that the bag will run out before Hallowe’en evening? (Assume that your first daily raids are on October 15th and your last daily raids are on October 31st.)

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, October 29, 2014 at noon Pacific Time.** I will post the answer shortly after.