> -----Original Message----- > From: Veech > We had a cash prize drawing at work today, awarding 12 cash prizes to > employees in our division. There are 254 people in the > division, and 68 of > them were from my own staff. Remarkably, after drawing 12 > names, none of my > staff received a single cash prize. The names were written > on pieces of > paper and put in a box. The papers weren't folded, and the > whole process is > suspect. Anyway, before I make a stink to HR I wanted to know the > statistical probability of *none* of my employees being > chosen to win a > prize. I'm thinking it's about 1 in 50.
Let's look at the probability that someone NOT in your group wins. Probability = Number of people NOT in your group/total number of people First Pick: 186/254 = 73.2% Last Pick: 175/243 = 72.0% (assuming once the name is picked, it is not put back) So, the odds of a non staff member being picked remain at about 72.5% for all drawings. The larger group that does not include your staff will always have a higher chance of winning. I think you have fallen into the probability trap that assumes that the events are dependent on each other. Each drawing is in fact, independent of the previous drawings, so the chance of a non-staff member being selected is always the number of the non-staff members remaining divided by the total number of people remaining. See http://www.mathsrevision.net/gcse/pages.php?page=32 Hope this helps, Jim Maki [EMAIL PROTECTED]
