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/

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Anniversary Gift

Anniversary gifts: a year-by-year guide Anniversary gifts: a year-by-year guide Looking for a special present to celebrate your anniversary? Whether it's your first or your golden celebration, we've got hundreds of gift ideas for you. Let's just hope your man doesn't forget! First: paper Second: cotton Third: leather Fourth: linen Fifth: wood Sixth: iron Seventh: copper Eighth: bronze Ninth: pottery Tenth: tin or aluminium Eleventh: steel Twelfth: silk Thirteenth: lace Fourteenth: ivory Fifteenth: crystal Twentieth: china Twenty-fifth: silver Thirtieth: pearls Thirty-fifth: coral or jade Fortieth: rubies Forty-fifth: sapphires Fiftieth: gold Fifty-fifth: emeralds Sixtieth: diamonds First anniversary Traditional gift: paper Great gift ideas: Original edition of his daily newspaper from either the date he was born or your wedding date Write a love letter New book or an old edition of a book he loves Find an old postcard from a place that's meaningful for the two of you - the place you honeymooned, where he proposed or where you first met - and get it framed Adult board game Plane tickets Make a personalised calendar with pictures of the two of you, marked with all the dates that are important to the two of you (so he can't forget any) Decorate your home with Chinese paper lanterns Drawings, pictures or prints for your home Framed photo of you or of the two of you together Photo album filled with fun memories Gift voucher to his favourite shop Tickets to his favourite sporting event Second anniversary Traditional gift: cotton Great gift ideas: New bed linen Boxers or other attractive underwear for him Sexy cotton lingerie for you that both of you would enjoy Quality cotton towels Matching dressing gowns Hammock Personalised T-shirt Third anniversary Traditional gift: leather Great gift ideas: Leather clothing Leather shoes Leather-bound notebook Leather briefcase Leather wallet Leather belt Mobile phone in a leather case Leather gloves Leather desk set Leather luggage Leather watch Fourth anniversary Traditional gift: fruit or flowers Great gift ideas: Have flowers or a fruit basket delivered to his office Make a garland of flowers and wear just that for each other Share a bubble bath and light the room with floral-scented candles Sprinkle rose petals all over your bed Share a delicious fruity cocktail Fifth anniversary Traditional gift: wood Great gift ideas: Bonsai plant Weekend away in a log cabin Wood plaque engraved with words of love Take a walk in the woods Photo of you or of the two of you in a wooden frame New fence or decking Wooden furniture Wood sculpture or carvings Sixth anniversary Traditional gift: iron Great gift ideas: Golf clubs Iron sculpture Gym membership (get him pumping iron!) Wrought iron outdoor furniture Iron skillet, if he likes to cook New iron, if he likes to iron Trip to Paris to visit the Eiffel Tower CD by Iron Maiden, if he's a fan DVD of The Iron Giant Tools and hardware Wrought iron bed Seventh anniversary Traditional gift: wool or copper Great gift ideas: Cashmere or good wool scarf, socks or jumper Blanket to snuggle under together New suit Outing to a sheep farm Woolly hat New coat to keep him warm Copper kettle or cookware Copper fireside accessories Copper sculpture Eighth anniversary Traditional gift: bronze Great gift ideas: Hand-held bronze bell Bronze sculpture or figurine Day trip to the beach to catch some sun Sun tan lotion for a tropical dream holiday Ninth anniversary Traditional gift: pottery Great gift ideas: Re-enact the pottery scene from Ghost! Join a pottery class together Coffee mug Plant pot, vase or bowl Figurines for the lawn Tenth anniversary Traditional gift: tin or aluminium Great gift ideas: Personalised number plate Digital camera Tin of caviar or foie gras Tin toy airplane or car Tin sign for his office or study Aluminium watch Eleventh anniversary Traditional gift: steel Great gift ideas: Engraved key chain CD by Steel Pulse Stainless steel watchband Calypso steel drum Ice skates Stainless steel cookware Stainless steel cocktail shaker or ice bucket Steel-coloured sunglasses Trip on the London Eye Twelfth anniversary Traditional gift: silk or linens Great gift ideas: Lingerie for you (for him to enjoy!) Silk robe, shirt, suit, sheets, boxers or tie Nice new razor - to make him smooth as silk! Silky smooth bubble bath Linen tablecloth with matching napkins New bed linen Linen suit Thirteenth anniversary Traditional gift: lace Great gift ideas: Handkerchief Lacy slips or underwear for you Lace tablecloth Fourteenth anniversary Traditional gift: ivory Great gift ideas: Piano - classic or electric Trip to the Ivory Coast of Africa Ivory bed linen An ivory coloured shirt or tie Personalised ivory writing paper or cards Fifteenth anniversary Traditional gift: crystal Great gift ideas: Glasses filled with Cristal champagne Crystal decanter Crystal vase or candlesticks Billy Crystal DVD such as When Harry Met Sally Trip to the mountain for skiing or relaxation Swiss watch with a crystal face Twentieth anniversary Traditional gift: china Twenty-fifth anniversary Traditional gift: silver Great gift ideas: Frame filled with a photograph of you New watch Silver ornaments Silver pen Silver cufflinks or key ring Anything from Tiffany's silver collection Silver ring inscribed with actual wedding date and the present anniversary year Anniversary wedding band Trip to the movies - the silver screen! Thirtieth anniversary Traditional gift: pearls Great gift ideas: Oyster dinner (it's an aphrodisiac!) Pearl cufflinks Mother-of-pearl handle, e.g. shaving brush or coat brush Mother-of-pearl mosaic photo frame Thirty-fifth anniversary Traditional gift: coral Great gift ideas: Scuba trip or scuba lessons Trip to Coral Gables, Florida Trip to the Great Barrier Reef, Australia Coral-coloured tie Coral cufflinks Fortieth anniversary Traditional gift: ruby Great gift ideas: Have rubies put into your wedding bands (one for each of your children, or the number that corresponds to your anniversary month or wedding date) A dozen ruby-red roses Ruby-red theme party A bottle of vintage red wine Forty-fifth anniversary Traditional gift: sapphire Great gift ideas: Sapphire tie clip or cuff links Sapphire-coloured item of clothing Bottle of Bombay Sapphire gin Fiftieth anniversary Traditional gift: gold Great gift ideas: Favourite golden oldies (CD collection) Gold jewellery Gold watch Gold theme party Fifty-fifth anniversary Traditional gift: emerald Great gift ideas: Trip to the Emerald Isle (Ireland) Emerald-studded cufflinks Emerald-coloured silky boxers Sixtieth anniversary Traditional gift: diamond (also for 75th) Great gift ideas: Diamond jewellery Something very special to celebrate making it this far!

birthday gift idea, or

50th, 40th, 60th birthday gift ideas For that special 40th birthday gift idea, 50th birthday gift idea or 60th birthday gift idea, or just because you want to; why not treat him to a birthday gift he will never forget . A birthday break on four wheels! Cornwall Classic Car Hire has developed a special gift service ideal for that memorable birthday when you need something really special to mark the big day.or, if you are trying to buy for the man who appears to have everything , Birthday Breaks offers the solution. Why not take him away from it all on a romantic classic car break in Devon or Cornwall? Great as a source of ideas for unusual male presents our special gift service recognises the fact that after a while socks, ties or even surprise parties have had their day, so let him live his dreams with a weekend away in a classic sportscar. We offer a fine range of classic British sportscars as either car hire only or as an inclusive classic car break. We work with an excellent selection of accommodation partners to ensure you enjoy an outstanding birthday break together. What better venue could there be than the beautiful scenery and coastline of Devon & Cornwall as a romantic birthday setting? Alternatively, as a special birthday present for Dad, a hire of a classic British sportscar is really hard to beat! Whether you book for your Dad or partner, the men in your life cannot fail to be touched by the gift of driving a classic British sportscar. We offer the cars most people would love to own!. Choose from our: Legendary E Type Jaguars... MKII Jaguar - made famous by Inspector Morse Triumph Stag 3 Litre convertible Superb swept-wing MG TC Austin Healey 3000 Sixties two seater Austin Healey 3000, Triumph TR4A or MG B V8 Roadster If he is about to celebrate a fortieth, fiftieth or sixtieth, when you really want to make a fuss of him, why not let him drive the E-type Jaguar he always aspired to own? Or perhaps the chance to reminisce about the good old days of motoring in the MG TC would be just the ticket? At the end of the day we all know men just love their motors! Go on... make someones birthday - hire them the classic car of their dreams! Find out how it works... Home | Our Service | About Us | News | Contact us | Our Cars | Testimonials | Site Map Discover Cornwall | Cornwall's Motoring Heritage | Terms and Conditions | Admin Honeymoon Ideas | Anniversary Gift | Birthday Gift Ideas | Recommended Sites Email This Page to a Friend --© Classic Escapes Limited 2004. Classic Escapes Limited operates the licensed brand names of Classic Escapes , Cornwall Classic Car Hire and Devon Classic Car Hire . Powered by KernowStore --

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