You've probably heard that in a group of about two dozen people there is a high chance that at least two of the people have the same birthday anniversary. If you've ever wondered why this is so, keep reading. The calculation of probabilities where multiple events are involved can be a daunting task. So, this particular poser has been reduced to a relatively simple calculation and is based on the following relationships:
the total probability of all possible events occurring is equal to one (1)
it is possible to calculate the probability of a particular event (e. g., no occurrence)
subtracting the calculated probability from one gives the probability of at least one occurrence
So, in order to calculate the probability that, among a group of people, at least two of them have the same birthday anniversary, all we have to do is calculate the probability that none of them have the same birthday anniversary and subtract that from one (1). Start with one person in the room, we'll call her Amanda. The probability that her birthday anniversary is unique among all the people in the room is one; after all, Amanda is the only person in the room! Now, let Brenda enter the room. The probability that Brenda's birthday anniversary is different from Amanda's is 364/365 (we'll ignore leap years in all of this) since there are 364 available days other than Amanda's birthday. With just two people in the room, the probability that they do not share a birthday anniversary is 1 x (364/365) or 0.997 and the probability that they share a birthday anniversary is 1 - 0.997 or 0.003. In walks Carla. In order for Carla's birthday anniversary to be different from either Amanda or Brenda, it must occur on one of the remaining 363 days. The probability that Carla does not share a birthday anniversary with either Brenda or Amanda is 1 x (364/365) x (363/365) or 0.992. And, the probability that at least two of the three people share a birthday anniversary is 1 - 0.992 or 0.008. We can continue this calculation as each new person enters the room and this is shown graphically below. Shown in red is the probability that no two people share the same birthday anniversary {1x(364/365)x(363/365)x ...} for 2 to 50 people. The green line is the probability that at least two people share a birthday anniversary. You can see that with 23 people in the room, the green curve has reached a probability of about 0.5 (0.507). This means there is a 50% chance (even odds) among a group of 23 people that two of them have the same birthday anniversary .www.ddhw.com
My thanks to a visitor who pointed out that this problem concerns the probability that two people share the same birthday anniversary or celebrate their birthday on the same day of the year.
哈哈哈哈 O(∩_∩)O哈哈~ 好久不来了，不小心看了一眼自己主页，发现自动关联了自己以往发过的帖，点进这个看了一眼，笑个半死。。。敢情我当初还发过这么搞笑的东西啊，我自己完全不记得了 
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发表于 2006-3-21 05:00:45
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给俺点信心吧，俺成了大财主后请脑坛的朋友吃香的喝辣的 
发表于 2006-3-21 08:02:53
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