Of course, you can expand the sample space to include more slips of papers (i.e. Let be the number of selections that are required to perform this random experiment. Keep drawing until all 12 numbers have been chosen. Randomly draw a piece of paper and note the number and then put it back into the hat. Put 12 slips of papers numbered 1 through 12 in a hat. The random experiment that has been described is this. On average, you will have to ask about 37 people to get the entire set of 12 animals. So the overall average is not a number near 12. For example, if you have encountered 11 animal signs already, you will have to ask on average 12 more people to find the last animal sign.
As you encounter more animal signs, it takes longer to get a new animal sign. As you ask more people, the animal signs tend to repeat. It turns out that the first few animals are easy to obtain (just like in the meeting with 4 different animal signs for 4 people). It is almost certain that you have to ask many more people. The outcome of twelve people is not likely (it has only about 0.005% chance of happening). If you are very lucky, you may encounter all 12 signs by asking just 12 people (the minimum number of people you have to ask). The number of people you have to ask is a random quantity. How many people do you have to ask in order to have met all 12 animal signs? Imagine that you keep picking people at random and ascertain his/her animal sign. It turns out that a pig is also represented. Another coworker did not know his sign and Googled to find out that he is a rat! Another coworker is a rooster. What better way to celebrate the year of the rooster than working a related math puzzle, or to perform a related random experiment!Īt the office yesterday, conversation at the beginning of a meeting, before discussing the main topics, centered on the Chinese zodiac animal signs (the Chinese zodiac system is a 12-year cycle with a different animal representing each year). In fact, today (January 28, 2017) is the start lunar New Year, which is the first day of the year of the rooster. According to the Chinese zodiac, the year 2017 is the year of the rooster.