This document discusses probability and uses the birthday problem to calculate the probability of two or more passengers on a flight having the same birthday. It finds that with 20 passengers there is a 41.15% chance of a match, with 30 passengers the chance is 70.63%, and with 40 passengers the chance is 89.12%. Running these probabilities over 6 flights per month, it estimates the airline could expect to award around 2.5, 4.2, or 5.4 prizes per month depending on passenger loads. It concludes the marketing director's assessment of a 10.95% chance of a match for a full flight was inaccurate.