Birthday Present
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Math Forum: Ask Dr. Math FAQ: The Birthday Problem -- Ask Dr. Math: FAQ The Birthday Problem Dr. Math FAQ || Classic Problems || Formulas || Search Dr. Math || Dr. Math Home Suppose you flip a coin and bet that it will come up tails. Since you are equally likely to get heads or tails, the probability of tails is 50%. This means that if you try this bet often, you should win about half the time. What if somebody offered to bet that at least two people in your math class had the same birthday? Would you take the bet? This question is more complicated than flipping a coin, because the chance of finding two people with the same birthday depends on the number of people you ask. If there were only one other person in your math class, you might be surprised to find out that she had the same birthday as you. If there were a pair of people with the same birthday in a class of 366 people, would you still be surprised? How large must a class be to make the probability of finding two people with the same birthday at least 50%? Let's forget about leap year when we solve this problem (no February 29 birthdays!) This way, we can assume that a year is always 365 days long. We'll start by figuring out the probability that two people have the same birthday. The first person can have any birthday. That gives him 365 possible birthdays out of 365 days, so the probability of the first person having the "right" birthday is 365/365, or 100%. The chance that the second person has the same birthday is 1/365. To find the probability that both people have this birthday, we have to multiply their separate probabilities. (365/365) * (1/365) = 1/365, or about 0.27%. Now, what about three people ? The chance of the first and second person sharing a birthday is still 1/365. The first and third person might share a birthday instead. The probability of that is 1/365 as well. But what if the second and third person shared a birthday? And what if all three of them had the same birthday? Things are getting complicated fast. Four or five people would be even messier. Is there a simpler way? To solve the birthday problem, we need to use one of the basic rules of probability: the sum of the probability that an event will happen and the probability that the event won't happen is always 1. (In other words, the chance that anything might or might nothappen is always 100%.) If we can work out the probability that no two people will have the same birthday, we can use this rule to find the probability that two people will share a birthday: P(event happens) + P(event doesn't happen) = 1 P(two people share birthday) + P(no two people share birthday) = 1 P(two people share birthday) = 1 - P(no two people share birthday). So, what is the probability that no two people will share a birthday? Again, the first person can have any birthday. The second person's birthday has to be different. There are 364 different days to choose from, so the chance that two people have different birthdays is 364/365. That leaves 363 birthdays out of 365 open for the third person. To find the probability that both the second person and the third person will have different birthdays, we have to multiply: (365/365) * (364/365) * (363/365) = 132 132/133 225, which is about 99.18%. If we want to know the probability that four people will all have different birthdays, we multiply again: (364/365) * (363/365) * (362/365) = 47 831 784/ 48 627 125, or about 98.36%. We can keep on going the same way as long as we want. A formula for the probability that n people have different birthdays is ((365-1)/365) * ((365-2)/365) * ((365-3)/365) * . . . * ((365-n+1)/365). If you know permutation notation, you can write this formula as (365_P_n)/(365^n). That's the same as 365! / ((365-n)! * 365^n). We've made some progress, but we still haven't answered the original question: how large must a class be to make the probability of finding two people with the same birthday at least 50%? We know that the probability of finding at least two people with the same birthday is 1 minus the probability that everybody has a different birthday, and we know how to find the probability that everybody has a different birthday for any number of people. The easiest way to find the right class size is to use a calculator to try different numbers in the formula. It turns out that the smallest class where the chance of finding two people with the same birthday is more than 50% is... a class of 23 people . (The probability is about 50.73%.) From the Dr. Math archives: Probability Theory: Coincidental Birthday Probability of the Same Birthday within a Group Birthday Probabilities Three Share a Birthday The Birthday Problem; Queuing at a Bank Birthday Probability, Class of 25 One Person of Seven Born on Monday Odds of Left-Handedness in a Group From the Web: The Birthday Problem: A short lesson in probability , George Reese A Java applet that you can use to test different class sizes (it works better with small classes) and graphs of the probability for different numbers of people. The Law of Small Errors , Keith Devlin The birthday problem, and related questions - what's the probability that someone will have your birthday? Birthday Surprises, Ivars Peterson Birthday Problem, Eric Weisstein's World of Mathematics Coincidence, Alexander Bogomolny How to Read Mathematics, Shai Simonson and Fernando Gouveau This article uses an explanation of the birthday problem as an example. An Introduction to Mathematica and the "Birthday Problem," Louie Beuschlein For a general review of probability: Probability, Dr. Math FAQ Probability in the Real World, Dr. Math FAQ - Ursula Whitcher, for the Math Forum Submit your ownquestion to Dr. Math [ Privacy Policy ] [ Terms of Use ] Math Forum Home || Math Library || Quick Reference || Math Forum Search Ask Dr. Math ® © 1994-2005 The Math Forum http://mathforum.org/dr.math/
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50th Birthday Gifts - Candy you ate as a kid - My account -Contact us -Home Ordering info -Shop for candy -Candy pictures -Candy store list -Sugar-free candy -Gift Certificates -Kosher Candy - wholesale prices -Ordering Q & A Candy Gifts -It's a boy - It's a girl -Halloween gifts -30th birthday gifts -40th birthday gifts -50th birthday gifts -60th birthday gifts -Any birthday gifts -Any occasion gifts -Gift cards Shipping info -Shipping Q & A -Hot weather shipping -Free shipping for APO and FPO orders -Rush orders, PLEASE click here! Candy info -Vote for your favorite candy -Candy pictures -Discontinued candy & gum Other stuff -Tell a friend about us -Subscribe to our newsletter -About us -Testimonials Links -Link Exchange -Links of interest -Affiliate Program -Home 50th Birthday Gifts Candy you ate as a kid from the 60s! Your search for that special gift is over Each 50th birthday gift assortment is packed with popular candies from the decade of Beatles, hippies, flower power, lava lamps and bell-bottom pants. Candies such as Wax Lips, Candy Cigarettes, Necco Wafers, Candy Buttons on paper tape, BB Bats, Kits, Wax Bottles with flavored syrup, Astro Pops, Hot Dog gum, Now & Laters and many more fresh old fashioned candies from the 60s. 50th birthday gifts... click here to order. In our family a birthday with a "zero" is a very special birthday. We know how hard it is to find a gift for that special person. Please consider Candy you ate as a kid from the 60s. One size fits all and everyone loves candy. Inside the candy box... click picture to see an expanded view. Personalized candy box top... click picture to see an expanded view. Make your gift special with a personalized box top message. 50th birthday gifts... click here to order. Here is a typical 60s Candy you ate as a kid assortment... 100 Grand Bar, 5th Avenue, Anise Squares, Astro Pops, Atomic Fire Balls, Bazooka Bubble Gum, BB Bats, Bit-O-Honey, Black Taffy, Boston Baked Beans, Bubble Gum Cigars, Butterfingers, Candy Buttons, Candy Cigarettes, Candy Necklace, Carmel Creams, Charleston Chews, Charms, Chick-o-Sticks, Chiclets, Chuckles, Cinnamon Bears, Dots, French Chew Taffy, Gold Mine Gum, Good & Plenty, Hot Dog Gum, Indian Brand Pumpkin Seeds, Jaw Breakers, Jelly Nougats, Jujubes, Jujyfruits, Junior Mints, Kits, Lemonheads, Life Savers, Long Boys, Mary Janes, Necco Wafers, Nik-L-Nips, Now & Later, Pay Day, Peanut Butter Bars, Planter's Peanut Bar, Rainblo Gum, Red Hots, Red Vines, Root Beer Barrels, Saf-T-Pops, Sen Sen, Sixlets, Sky Bar, Slap Stix, Slo Pokes, Smarties, Smith Brothers Cough Drops, Sourballs, Sugar Baby, Sugar Daddy, Swedish Fish, Sweet & Sour Pops, Sweetarts, Teaberry Gum, Tootsie Pops, Tootsie Rolls, Vanilla Caramels, Walnettos, Wax Lips, Whoppers and Zagnut. Each 4 pound assortment is jammed with over 70 of your old time favorites. The box contains over 60 different candies with some duplicates. The actual assortment you receive will vary with availability from our suppliers. Not all candies are included in every assortment. Build your own bag of Candy you ate as a kid on our Pack-a-Bag page. 50th birthday gifts... click here to order. Testimonial... I meant to write sooner - but I just wanted to tell you about another very happy customer. I sent a box to my sister for her birthday and she was thrilled! She called me even as she and her daughter were doing the initial pawing through the goods! If I know my sister, she'll soon be ordering and sending these to her friends. Thanks again for the box of memories. Susan Testimonial... Hi Karen, Thanks so much for making our birthday so much fun!! We celebrated tonight, and I must say, that my sister was truly speechless when she opened her box of goodies!! Then, she went through everything piece-by-piece and we shared our special little memories as kids. Karen, your candy is not just candy...it's like a springboard into the past where we can relive some of the best times of our lives when children. The good memories we connect with each type of candy is amazing! We talked of certain types of candies and how they reminded us of such happy times with particular relatives and friends...truly medicine for the heart and soul! Here are the pictures I told you I'd try to send. Sure hope they come through for you. If you have a problem, just let me know and I'll be happy to resend them! God Bless You all and Thanks Again! Terri Home / Privacy Policy / 100% Money-Back Guaranty / Shop for Candy / Shipping Info / Affiliate Program 2000 - 2005 by the Old Time Candy Co. All rights reserved. 25222 Sprague Road - Olmsted Falls, Ohio 44138 - 1-866-WAX-LIPS Candy you ate as kid is a registered trademark of the Old Time Candy Co. Have a question or comment? Contact Us To God be the glory, great things He hath done!