Mathematics Problem Of the Week

Fall 2007

POW #7

Willy Wonka and the Golden Tickets

Willy Wonka has once again put golden tickets into the wrappers of his famous chocolate bars. If you find a golden ticket, you are allowed to tour Willy Wonka’s highly secretive Chocolate Factory.

(a) In a box of 24 chocolate bars there are exactly 4 which contain a golden ticket. What is the probability that you first find a golden ticket in the wrapper of the 5^th chocolate bar that you purchase out of the box of 24?

(b) If there are N chocolate bars manufactured for this contest and g contain golden tickets, find an efficient general formula for the probability that the first golden ticket is found in the wrapper of the k^th chocolate bar that is purchased. You may use notation involving combinations, permutations and/or factorials to express your formula efficiently. As always, provide a justification for your answer.

Due Friday, October 26^th at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math/CS/Stat office or sent via e-mail to rlock@stlawu.edu.