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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..:: Housewarming Gift Basket :: Fair Trade and Socially Conscious Gifts Online ::.. Shopping Cart Customer Service Contact Us Privacy and Security Ordering and Shipping Fair Trade Coffee Shop Fair Trade Chocolate Gift Baskets Book Shop Crafts Clothing & Accessories Jewelry Bath and Beauty College Shop Shop by Region Global Exchange Originals Gift Certificates Donate/Memberships Coffee Shop Fair Trade Coffee Fair Trade Tea Fair Trade Chocolate Gourmet Foods Book Shop Books Films Audio Book Shop Gifts Crafts Kitchen and Dining Home and Garden Bath and Beauty Candles and Incense Stationery and Journals Chimes and Musical Instruments Dolls and Toys Clothing and Accessories Clothing and Sneakers Bags and Wallets Jewelry Shop Earrings Necklaces and Bracelets Rings and Pins Jewelry Boxes and Accessories Men's Jewelry Shop by Birthstone Gift Baskets Recipient Baskets Occasion Baskets Gourmet Gift Baskets Gift Packs All Gift Baskets For Her For Him College Students Kids and Baby Wedding and Anniversary New Baby Birthday Holiday Housewarming Under $50 $50-$75 $75+ Ordering and Shipping Customer Service Frequently Asked Questions Get Involved Press Room Gift Registry | Corporate Gift Program | Affiliate Program | About Fair Trade | About Us Home > Shop by Price > $75+ > Housewarming Gift Basket Housewarming Gift Basket Shower new home dwellers with this unique combination of essential housewares. A natural hand-woven kaisa grass basket from Bangladesh is filled with: An Applique Potholder from Nepal Vetiver Sachets from Indonesia Decorative Metal Hook from Haiti Set of three Dishclothes from Nepal Two Hand-painted Ceramic Mugs from Thailand Certified Fair Trade and Organic Choice Tea (Your choice of flavor) Napkin Holder from El Salvador Tablerunner from Nepal Every Item has a story : We include a card with our items to share the story behind what makes each one special. [ read the story ] $99.00 Item Code: GB6012 Quantity Choose a Choice Tea CT Orange Spice CT Darjeeling CT Asian Blend Green CT Jasmine Green CT Green Moroccan Mint CT Earl Grey CT Irish Breakfast CT English Breakfast CT Black CT Decaf Earl Grey CT Decaf Green CT Decaf Mango Ceylon Our checkout process is secure and encrypted. Learn more . What will my shipping cost? Related Items: Hemp Potholder Ovenmitt Set $15.00 Obeechi Wood Salad Bowl & Accessories Dhukuti Placemat & Napkin Sets from Nepal JavaScript is currently disabled in your browser, so we cannot check your current cookie-enable setting. Our shopping cart requires cookies to be enabled in order to remember all the items in your cart. If you have trouble adding items to your shopping cart , click here to learn how to enable javascript and cookies in your browser or call us at (800) 505-4410. Global Exchange Implements the principles of socially and economically responsible business by operating according to Fair Trade Criteria. Shopping Cart | Customer Service | Contact Us | Privacy and Security | Ordering and Shipping Gift Registry | Corporate Gift Program | Affiliate Program | Get Involved | About Fair Trade | About Us © Global Exchange 2004 - 110 Capp Street, 2nd Floor - San Francisco, CA 94110 t:800-505-4410 f:415-861-0600
shower gifts. 1. Diapers,
Baby shower gift ideas Baby shower gift ideas Baby shower gift ideas for the Mother-to-be that already has one - or more - children, from experienced moms. When you go to a baby shower for a first time mom, it’s so much fun to shop. After all, you know that she needs almost everything! Shopping for pregnant friend who already has one (or more!) kids is more challenging – after all, how do you know what she already has, likes or needs? If she knows the gender of the baby, she’s sure to get clothes, especially if she’s having a different sex than her first-born. Here are some tips compiled from several mothers of their favorite second-time baby shower gifts. 1. Diapers, wipes and lotions. This isn’t the most romantic of gifts, but most second-time moms tell us that this is a practical and always-appreciated gift. A package or two of newborn-sized diapers, sensitive skin baby wipes and lotion make a great gift basket! 2. Board Books are always a hit for children. Good sturdy backed board books can survive chewing, drooling and dropping, and are nice for young children of all ages! Look online for some suggestions or try these tried and true favorites: Good Night Moon, Moo Moo Peekaboo, Time for Bed, The Mitten, Mouse Count, and The Cheerio Play Book. 3. A soft blanket or unique stuffed animal is always a welcome touch. Most children bond to one special “lovey”, so look for something soft and unique. One nice idea is the blanket/animal combinations made by Stephen Industries, like the bunny blankets – a soft stuffed bunny rabbit head, with a blanket body, ready to be loved and cuddled. One source for this is http://www.bkpuffnstuff.com/nursery.htm. 4. Frozen Dinners are always a hit for second time moms. It’s hard enough to prepare a meal for the family when you only have one child at home, with the addition of a second (or more) time becomes even more precious! Bring two or three clearly labeled frozen dinners for her freezer. Be sure to write the contents and preparation instructions clearly on the outside, so she can tell at a glance what it is and how to make it. Using a disposable foil pan will eliminate any anxiety about returning the dishes, as well! 5. A Babysitting Certificate for the older child(ren). Offer to take her older kids out for a day – or two – after the baby arrives. She’ll appreciate the thought but probably be too embarrassed to initiate this, so just plan on calling her the week after the baby arrives to schedule your day. If you work, you can always offer to take the child(ren) on a Saturday afternoon, or after work for an evening. You might even consider scheduling a standing appointment – every Wednesday evening, for example, for a month – that way she can plan and prepare for her “free time!” 6. Picture frames and photo albums are always a welcome touch. If you’re a scrapbooker, you might also want to offer to make a scrapbook for her of baby’s first year, collecting photos and making special pages that you return for her to include in her album. 7. A Double Stroller is always a fabulous gift if there are other young children in the home. Check online resources like Epinions (research.epinions.com) to see what brands are recommended for the ages of her children. 8. A Gift for Mom is always a nice and personal touch. A gift basket with self-pampering items like lotions, a nice nightgown, home facial items, etc. will make her feel pretty and appreciated. If you give a gift certificate make it specific, like for a facial or a manicure/pedicure. 9. A fold-up Booster seat is a fabulous gift if she doesn’t already have one. These are travel high chairs but also double as secondary high-chairs at home if she has other little ones who still need a boost – and free up the regular high chair for the new arrival! 10. A Housekeeper Visit. If you can afford an outside housekeeper, give her a gift certificate for them to come and clean her house after the baby arrives. This will help relieve her of some of the drudgery that adds more demands on her time! If you can’t afford an outside housekeeper, consider offering to do this yourself. Bear in mind that like the babysitting, she’ll probably be embarrassed to take you up on this, so you’ll have to call to schedule this after the baby. Don’t take no for an answer, either – find a time that works for her, and just show up ready to work, with all of your own supplies if possible (that way you won’t have to bother her to ask where her broom, vacuum, cleanser, etc. are). Run a couple loads of laundry, clean her bathrooms and kitchen, and give her carpet a good cleaning and she’ll be thankful for life! When in doubt, a gift certificate to a nice children’s store such as the Right Start Store (which offers a great selection of unique kids products and has online shopping as well!) will always be appreciated. The most important thing is to have fun, and realize that every baby is a blessing! Happy Shopping! © 2002 Pagewise You are here: Essortment Home >> People & Culture >> Holidays:Gifts >> Baby shower gift ideas << Great gifts for school teachers Creative gift wrapping ideas >>
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