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Professor Young H. Chun
The "Solution" to the Birthday Problem?
Go Tigers!

   The following amusing textbook "solution" to the birthday problem was circulating on the Isolated Statisticians electronic discussion group. The title of the book is "Developing Creative & Critical Thinking", the author is Robert Boostrom, and the publisher, National Textbook Company. The following is from pp. 102-103:

   "Suppose that there were only two people -- you and one other person in the class. The chance that you and the other person have the same birthday is approximately 1 in 365. ...  

   Now, add a third person. The chance that the birthday of the third person will match yours or the other person's is 2 in 365. Next, add a fourth person. ...

   Continuing in this way, you end up with twenty-nine ratios that can be added in the way that fractions are 1/365 + 2/365 + ... + 29/365.

   Therefore, the probability of two people in a group of 30 having the same birthday is 435/365. This very large ratio means that it is almost certain that two people in any group of 30 will share the same birthday. Not only would you not be surprised to find out this was so, you would expect it."

  We got the exact reference from Linda Wagner, who encountered the text in the course EDUC W554 (Creative Problem Solving and Metacognition) at Indiana University-Purdue University at Ft. Wayne. The course counts for credit towards high school teaching certification! 

DISCUSSION QUESTIONS

(1) Using EXCEL, find the probability of at least one birthday match in a group of 30.

(2) Show that the author's calculation of 435/365 is correct for the expected number birthday matches in a group of 30.

(3) On the NPR program (Science Friday, May 29, 1998) mentioned above, the first caller remarked that his wife was two years younger and they both had the same birthday. He asked: What is the probability of that happening? How would you have answered him?

(4) The second caller remarked that obviously not all days are equally likely for birthdays. He commented that for humans they were probably not very different, but for animals they could be very different; and therefore we should be careful in our claim that 23 was correct. How would you have answered him?
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