Birthday Present

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/

golf gifts Home --

Executive Gifts with a Golf Theme golf gifts golf accessories barware golf art bar stools executive gifts Looking for the Perfect Gift for your Favorite Golf Loving Executive? golf desk clock sale $31.95 putter stand sale $97.95 golf ball pen stand sale $59.95 business card holder sale $29.95 golf desk lamp sale $129.00 golf club pen stand sale $59.95 golf business card holder sale $19.95 golf desk organizer sale $19.95 golf desk organizer sale $19.95 golf desk box sale $44.95 golf magnifiying glass sale $52.95 golf letter opener sale $44.95 business card case sale $21.50 desk pen sale $29.95 golf ball box sale $49.95 CD cabinet sale $67.95 golf bag pen pot sale $19.95 golf ball box sale $43.95 picture frame sale $15.95 golf desk lamp sale $59.95 golf bookends sale $29.95 golf desk lamp sale $61.95 vardon bookends sale $49.95 golf business card holder sale $15.95 4x6 picture frame sale $14.95 5x7 photo frame sale $19.95 golf valuables box sale $34.95 back to golf gifts Home -- site search HOME VIEW CART Gift Certificates Golf Tournaments 19th Hole Chocolate Golf Balls Cigar Shop Executive Gifts Accessories GPS Systems Figurines Furniture Novelty Practice/Instruction Stationary/Napkins Toys and Games Watches/Jewelry Under $25 Under $50 Under $100 home | contact us | policies | privacy | resources articles | sponsors | Misc. | partners | add url bar ware | golf board games | chocolate golf gifts cigar shop | executive golf gifts | golf accessories | golf art golf figurines | golf furniture | novelty golf gifts TheGolfCollection.com • (866) 626-9517 17330 West Center Road Omaha, Nebraska 68130 Cookie Jars | Online Degrees | Cookie Jars

Gifts for Men When

Gifts To Make For Men - Gifts BW gifts | gifts Resources | Add URL Wine Gifts & Baskets From the casual wine drinker to the serious enthusiast, we have a gift that will make them smile. Our selection includes premium wine, gourmet baskets, distinctive champagne sets & the very finest California and Northwest wines. Gifts To Make For Men Articles Gifts for Men When buying gifts for men remember they love to feel pampered and soothed after a long day of working. Gifts for men can run the gamut of fun things catering to their adventurous boyish side to more pragmatic things to assist in their everyday life....( Continue Reading ) Gifts for Men - Mummy Bags The mummy bag takes what is great about the traditional sleeping bag, and improves it through innovative features designed to capture heat and keep it inside the bag with you....( Continue Reading ) Frugal Gifts for Men Do you find it hard to come up with frugal gifts for men? Try these ideas....( Continue Reading ) Frugal Gifts for Men Do you find it hard to come up with frugal gifts for men? Try these ideas....( Continue Reading ) Great Gifts for Men Buying gifts for guys is not all that easy, especially when it seems they have everything they need. Browse this list of top picks and see the gadgets, cool items, and useful items that could make great gifts. See Also:......( Continue Reading ) Gifts To Make For Men Directory Links wedding gifts personalized unique office gifts fortune cookie gifts money tree gifts charleston gift baskets mothers day gift baskets ft lauderdale gift baskets uk gifts naughty valentines gifts great gifts for the family gift baskets alaska great valentines day gifts giving gifts gifts for your boss valentinesday gift baskets special times gifts recognition gifts girlfriend christmas gifts american baskets top 10 graduation gifts easter gifts for children japanese wedding gifts online christmas gifts pictures of gift baskets gift baskets of louisiana shop for hawaiian gifts cheap christmas gifts best gifts for christmas boyfriend christmas gifts wedding gifts for husband top 10 valentine gifts baby shower thank you gifts gifts baptism disc golf baskets corporate gifts recognition christian gifts for children elegant baby gifts birthday gifts ideas home interiors and gifts gift baskets in chicago 40th anniversary gifts top valentines gifts decorating easter baskets guy valentine gifts gifts for easter Popular Search Terms: Gifts BW © 2004 Gifts BW All trademarks are the property of their respective owners. All Rights Reserved. This site is not related to Brajeshwar or Brajeshwar.com in anyway, shape or form

Teacher Gifts Articles Top

Handmade Teacher Gifts - Gifts BW gifts | gifts Resources | Add URL Wine Gifts & Baskets From the casual wine drinker to the serious enthusiast, we have a gift that will make them smile. Our selection includes premium wine, gourmet baskets, distinctive champagne sets & the very finest California and Northwest wines. Handmade Teacher Gifts Articles Top Valentine's Day Gift Ideas From Visitors Check out these great St. Valentine's Day gifts shared by visitors just like you! Unique, home-made gift ideas for mom, dad, boyfriends, girlfriends, teachers, friends, anyone! Nothing quite says 'I Love You' like a personalized gift handmade by you....( Continue Reading ) Valentine's Day Gift Ideas Check out these great St. Valentine's Day gifts shared by visitors just like you! Unique, home-made gift ideas for mom, dad, boyfriends, girlfriends, teachers, freinds, anyone!...( Continue Reading ) Buy Crafts from Crafters Hand-made products on the Web, from handicrafts to fine art....( Continue Reading ) Biological Science Biology explorations and experiments to enlighten your students. Learn about the human body, plants, animals, fish, the rainforest and more....( Continue Reading ) 10 Gift Ideas for Single Mom's on Mother's Day The 10 gifts a single mom wants and needs most for Mother's Day...( Continue Reading ) Handmade Teacher Gifts Directory Links mothers day gifts ideas boyfriend christmas gifts gift baskets in los angeles unique wedding shower gifts romantic gifts for her 20 year anniversary gifts orlando gift baskets gifts in kind international gag gifts for christmas gifts for readers christian wedding gifts steves flowers and gifts sweet 16 birthday gifts gift baskets of alaska x mas gifts gifts for moms harbor house gifts graduation gifts for women florida fruit gifts halloween gift baskets gifts for 40th wedding anniversary make your own christmas gifts parents gifts wedding unique romantic gifts valentine day gifts gifts for your boyfriend spa gift baskets wedding favors gifts sewing baskets flowers and gifts great gifts for the family gifts for new teachers first anniversary wedding gifts gag gifts to make gifts for man graduation gifts ideas dbgt animated gifts macbirdie golf gifts girls birthday gifts gift baskets of virginia great gifts in 30 minutes gifts for fathers day christmas gifts in a jar personalized gifts for children gifts mothers day Popular Search Terms: Gifts BW © 2004 Gifts BW All trademarks are the property of their respective owners. All Rights Reserved. This site is not related to Brajeshwar or Brajeshwar.com in anyway, shape or form

Unique Gifts

Unique Wedding Party Favors, Wedding Favors, Gifts & ideas for Wedding, Bridal & Baby Showers, Friendship, Anniversaries & Memorials Help | Home | Contact Us Customer Comments | View Cart Enter Keywords Wedding Favors Gifts Attendants Gifts Engagement Parties Anniversary Ideas Bridal Shower Favors Gifts Decorations & Supplies Games Baby Shower Favors Gifts Decorations & Supplies Games Parties Birthday Celebrations Retirement Celebrations Party Ideas, Favors & Gifts Holiday Favors All Occasion Gifts Memorial Products Related Links Baby Shower Gifts Labor Day Pamper Pack Surprise your favorite Mommy-to-be with the gift of tranquillity on the one day she'll really need it! More Info Bridal Shower Gifts Newlywed Kitchen Combo Bride and groom oven mitts really get things cooking in the kitchen! Stir up some smiles with this fun novelty item. More Info Celebrate weddings , bridal showers , baby showers , anniversaries , friends and memorialize loved ones with special gifts and favors from The Rosemary Company. The herb rosemary is the symbol of remembrance, and a traditional gift for loved ones. It said they were someone special and would never be forgotten. Surprise your guests with an array of beautiful mementoes chosen for their thoughtful, unique and memorable qualities. Personalized Tea Favor Personalized Wedding Coffee Wedding Cake Candle Favor Long-Stemmed Lollies VIEW MORE WEDDING FAVORS Celestial Bridal Shower Favor Magnetic Clipboard Favor Bride To Be Button Cookie Cutter Heart Favor VIEW MORE BRIDAL FAVORS Personalized Baby Shower Notepads Showertime Baby Shower Favor Baby Bootie Shower Favors Satin Bunny Favor VIEW MORE BABY FAVORS Help | Home | Contact Us | View Cart © 2000 - 2005 The Rosemary Company. All rights reserved. Privacy Statement This site maintained by Fox Web Design Please direct all questions and comments to the Webmaster