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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/
Birthday Present At Days
18th Birthday Present - UK Guide Driving Days Flying Days Water Days Kids Days Pamper Days Newspapers Marriott Vouchers Unique Gift Ideas Corporate Email a Friend Ferrari Hire 18th Birthday Present At Days to Amaze we have some great ideas for 18th Birthday Presents. Choose from our wide selelection of activity gifts including flying a heicopter and white water rafting. The perfect gifts for any 18 year old. By offering our service on line, means we can update you with new experiences and offers regularly. Click here to see our whole collection of 18th Birthday presents This is just a sample of our 18th Birthday Presents Vauxhall Astra Rally gift experience day This has to be one of the best value for money full on rally driving experience's on the net. Get to grips with the Vauxhall Astra front wheel drive rally cars on a half day or full day format. You will learn the art of sliding through corners with controlled over steer, carrying out precise handbrake turns and more all on a mixed surface rally stage. After your gift experience each participant will receive a certificate of achievement and a trophy is awarded to the driver of the day-it could be you !!!(please note a full driving licence is required) Helicopter Flying Lesson If your are thinking about learning to fly a helicopter or even if you fancy something completely different and exciting then this is the one for you. After an initial briefing on controls and how the aircraft flies you take to the air and fly around the local area then its back to the airfield to practice low level flying and hovering. A perfect 18th Birthday Present and an ultimate dream day to remember. Kite Surfing Kitesurfing is the latest sport to take the world by storm. The sheer thrill as you accelerate through the wind is water is one of the most exhilarating experiences you can have. All kitesurfing courses are taught by International Kiteboarding Organisation / British Kitesurfing Association qualified instructors and we teach to set standards to ensure that you are given the best learning experience possible. Popstar Experience Here's your chance to prove your budding popstar status by recording your favourite song with YOU singing the vocals!!You will make a professional recording of one track which will be burned to CD on the day for you to take home.Use it for any occasion; just for fun, as a present for someone, or even for presenting a professional sounding demo to someone in the business! The Ultimate Makeover Experience This is a perfect 18th Birtday Present for any woman. The ultimate in make-over photography - includes a make-over, photo session and 4 5x7" portraits in a beautiful album. Start your Elegance Experience by discussing your colour preferences and any special requirements with your Make-up Artist, who will then apply your make-up and add the finishing touches to your hair as you sit back and relax. Next it's your Photo Session - it's posing time! Your Photographer will use a selection of fabrics with special lighting and posing techniques to create a stunning series of shots just for you. At your portrait viewing you'll have the chance to see the great results of your sitting, choose your inclusive 5x7" prints, and purchase any extra portraits required. For more 18th Birthday Presents click here Here at Days to Amaze our aim is to provide you with the best 18th Birthday Presents available anywhere online today. Our extensive range of 18th Birthday Presents and experiences have been carefully designed to provide the one you love with the perfect present they deserves. Browse through the selection of 18th Birthday Presents to find that special surprise - 18th Birthday Gift Ideas - 18th Birthday Presents - 21st Birthday Gift Idea - 40th Birthday Gift Idea - 50th Birthday Gift Idea - Activity Days - Activity Gifts - Adopt an Animal - Archive Newspapers - Birthday Gift - Birthday Gifts - Birthday Gifts For Her - Birthday Gifts For Men - Birthday Gifts For Women - Birthday Gift for Her - Birthday Gift for Him - Birthday Gift Idea - Birthday Gift Ideas - Birthday Newspapers - Birthday Presents - Birthday Presents for Boyfriends - Car Racing - Classic Car Hire - Corporate Activities - Corporate Activity Days - Corporate Event Activity - Corporate Team Building Events - Days Out - Drive a Ferrari - Drive a Porsche - Driving days - Driving experience - Driving experiences - Driving gifts - Ferrari Drive - Ferrari Driving - Ferrari Hire - Ferrari Rental - Flying Experience - Flying Experiences - Flying lessons - Gifts for Her - Gifts for Him - Gifts For Kids - Gifts For Men - Gifts For Women - Gift Days - Gift experience - Gift experiences - Gift Experience Days - Gift Idea - Gift Ideas - Gift Incentive Vouchers - Gift Man - Health Spa - Health Spa Days - Helicopter Flying Lessons - Helicopter Lesson - Helicopter Rides - Man Gift Idea - Off Road Driving - Old newspapers - Pamper and Spa Days - Pamper Breaks - Pamper Days - Pamper and Spa Breaks - Parachute Jump - Pilot School - Porsche Driving - Porsche Driving Experiences - Rally Days - Rally Driving - Rally Driving Schools - Rent a Ferrari - Spa Days - Spa UK - Team Building - Team Building Events - Team Building Exercise - Team building Midlands - Track Days - UK Team Building Events - Unique Gifts For Kids - Unique Gift Experience - Unique Gift Idea - Unique Gift Ideas - Powered by Ideal Internet
Housewarming Gifts Articles Ice
Good Housewarming 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. Good Housewarming Gifts Articles Ice Cream Sauces Add one of these to your ice cream to make it a complete dessert, from your About.com Guide...( Continue Reading ) Housewarming Gift Ideas: Continued Here are our favorite, and not so favorite gift ideas for housewarmings....( Continue Reading ) Housewarming Gift Ideas Moving into a new home is a time that's full of possibilies, and we often share in the excitement by taking a housewarming gift to the new homeowners. But what should you give? Here are our favorite, and not so favorite gift ideas for housewarmings....( Continue Reading ) A Housewarming Party A party plan for hosting a Housewarming Party with recipes and menu ideas....( Continue Reading ) A Housewarming Party A party plan for hosting a Housewarming Party with recipes and menu ideas....( Continue Reading ) Good Housewarming Gifts Directory Links hot holiday gifts things remembered personalized gifts retirement gifts for teachers coaches gifts organic baby gifts custom baby gifts gifts for 50th wedding anniversary 25th wedding aniversary gifts handmade mothers day gifts graduation gifts for girls ideas for mothers day gifts best christmas gifts 2002 valentine day gifts for guys gift baskets of delaware cheap gifts for guys gifts 2 india wicker storage baskets recipes for food gifts personalized golf gifts five year anniversary gifts online gifts to india 2nd anniversary gifts homemade teacher gifts gifts for father gift baskets cheese spiritual gifts from god birthday gifts by mail gift baskets chocolate japanese garden gifts anniversary gifts 10 year gifts for a girlfriend graduation gifts for nurses christmas gifts for mothers gifts for little girls gift baskets las vegas great grandmother gifts sterling silver baby gifts baskets gifts homemade wedding gifts beneva flowers and gifts gift baskets of texas biblical spiritual gifts bridal attendent gifts wholesale christmas gifts gift baskets for delivery 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
Gift Ideas MP3 Players
Amazon.com Computers:Gifts Your Store Computers See All 31 Product Categories   Your Account | Cart | Wish List | Help browse brands & products | top sellers | laptops & notebooks | desktops | computer add-ons | software | today's deals | outlet, used & refurbished Search Amazon.com Computers Refurbished Electronics Software Web Search Electronics > Gifts Browse Gifts by Type Desktops Digital & PC Cameras Handheld Accessories Inkjet & Laser Printers Laptop & Notebooks LCD Monitors Memory Cards MP3 Players Multifunctions Networking Photo Printers Pocket PC Handhelds Scanners Telephones & Accessories Browse Gifts by Price Up to $50 Up to $75 Up to $100 Up to $200 Up to $500 Browse Gifts by Brand Apple Canon Creative Labs Epson Hewlett-Packard Lexar Linksys Logitech Maxtor NEC-Mitsubishi Palm Samsung Sony Toshiba ViewSonic Viking Customers Rave Canon BCI-6PC Photo Cyan Ink Tank List Price: $11.95 Price: $9.79 You Save: $2.16 (18%) Used & new from $1.00 Watch out for that shipping charge from Amazon!! , September 4, 2005 Reviewer: Camera buff Of course this Canon ink is great. It would be interesting to know who in their right mind would pay $7.49 shipping for each ink cartridge. That's right, order 5 ink cartridges and pay $37.35 SHIPPING. I'm guessing Amazon doesn't really want to be bothered by selling this Canon ink. UPDATE... Read more Stumped? Not sure what to give the person who seems to haveeverything? Send them an Amazon.com giftcertificate , and let them choose the gift of their dreams. Your Friends' Wishes Find a Wish List Enter Name or E-mail Location (optional) Great Gift Ideas MP3 Players Creative Zen Micro 5 GB MP3 Player Silver Creative Zen Touch 20 GB MP3 Player View all selections Handhelds Garmin iQue 3600 GPS Auto Bundle Garmin iQue 3600 PDA/GPS Handheld System with Americas Detailed Street Mapping View all selections Inkjet and Laser Printers HP LaserJet 1320 Monochrome Laser Printer HP DeskJet 9650 Color Printer View all selections Game Hardware Logitech Dual Action Game Pad USB Logitech MX 510 Performance Optical Gaming Mouse (Red) View all selections Our Top Sellers Updated Hourly 1. Apple 20 GB iPod M9282LL/A by Apple Computer Price: Click for price Used & new from $209.99 2. Linksys WRT54G Wireless-G Router by Linksys Price: Click for price Used & new from $55.00 3. Netgear WGR614 802.11g Wireless Router by Netgear Price: Click for price Used & new from $36.00 4. Viking 256 MB Secure Digital Flash Card (SD256M) by Viking Components Price After Rebates: $11.49 Used & new from $20.00 5. Plantronics DSP-500 Digitally-Enhanced USB Gaming/Multimedia Stereo Headset and Software by Plantronics Price: $46.94 Used & new from $44.89 More top sellers Where's My Stuff? Track your recent orders . View or change your orders in Your Account . Shipping & Returns See our shipping rates & policies . Return an item (here's our Returns Policy ). Need Help? Forgot your password? Click here . Redeem or buy a gift certificate. Visit our Help department . Search Computers Electronics All Products for Top of Page Amazon.com Home | Directory of All Stores Our International Sites: Canada | United Kingdom | Germany | Japan | France  | China Contact Us | Help | Shopping Cart | Your Account | Sell Items | 1-Click Settings Investor Relations | Press Releases | Careers Conditions of Use | Privacy Notice © 1995-2005, Amazon.com, Inc. or its affiliates