Problem Coins
Posted in Uncategorized on 06/23/2003 08:02 pm by admin
Problem Coins
 |
 2012 CANADIAN 1 CENT FINISH MS 65 NC  US $3.89
|
 2012 CANADIAN 5 CENTS FINISH MS 65 NC US $3.40
|
 2008L CANADIAN 25 CENTS FINISH SPECIMEN US $2.43
|
 1969 CANADIAN ONE DOLLAR BU NICKEL US $2.89
|
 BIRTH YEAR 1954 Proof set problem free coins 921n US $169.00
|
In the introductory article we introduced the concept of probability being a mathematical measure of the likelihood of an event occurring. This was illustrated with the tossing of a single coin, in which case the probability of it landing as a head is 1 in 2 (also expressed as 0.5) and the probability of it landing as a tail also 1 in 2 (0.5). When tossing a single coin, the possible outcomes are mutually exclusive - the coin cannot land as a head and a tail at the same time. The laws of probability state that the sums of the probabilities of each possible outcome must, therefore, equal 1.
In this second article in the series, we are going to continue to look at coin tossing, but by introducing more that one coin we will significantly increase the complexity of mathematics required to calculate the probability of individual events.
First, take two 10 pence coins and throw them a few times, asking the kids to record the outcome of the throws. There appear to be three possible outcomes to tossing two coins: two heads, two tails or a head and a tail. However, swap one of the coins for a 50 pence coin and repeat the exercise, again asking the kids to record the results. There are now four possible outcomes: two head, two tails, the 10p as a head and the 50p as a tail, or finally the 10p as a tail and the 50p as a head. If one were to record the results as a grid, it would look like this:
10p - 50p
H - H
H - T
T - H
T - T
By using two different coins, you reveal an additional outcome that using identical coins had concealed. When calculating probability, coin 1 being a head and coin 2 a tail is a different outcome to coin 1 being a tail and coin 2 a head, even if the two outcomes can't be distinguished visually. In the case of tossing two coins, one of the four outcomes is two heads, so the probability of this occurring is 1 in 4 (0.25). Similarly, the probability of throwing two tails is 1 in 4 (0.25). However, the probability of throwing a head and a tail is 2 in 4 (0.5), since two of the outcomes have one head and one tail, although it is a different coin which is the head in each case. Reassuringly, the sum of all the possible outcomes, 0.25 + 0.25 + 0.5, equals 1 as we would expect.
Probability may work as an abstract concept for kids, but the thing that really engages them is being shown practical applications for the subject.
The Odd Sock Problem
In this practical exercise, kids work out the probability of choosing a pair of socks of matching colour if they can't see the socks from which they have to choose. It mimics a real life problem that many blind people experience when getting dressed. Get one pair of red socks and one of green, separate them so there are four individual socks and put them in a bag. Next, get the kids to work out the probability that two socks drawn from the bag at random will make a matching pair.
There are two approaches to working out the probability in this case. The first involves gridding out all twelve possible outcomes and counting how many of the twelve include a matching pair. The second approach uses a logical short cut which says that the colour of the sock we draw first is immaterial, so long as we can calculate the probability that the second sock we draw is of a matching colour. It's worth pointing out that many kids will conclude that the sock problem is identical to the situation where one is tossing two coins. However, there is an important difference between the two situations which means that the probability of throwing two heads is not the same as drawing both green socks.
In the concluding the article in the series we'll consider how the sock problem differs from the coin tossing scenario and work through the two approaches to calculating the probability of drawing matching socks from the bag. To reinforce the theoretical learning, the group can carry out a practical experiment to determine whether the actual results of drawing socks at random matches the predicted probability. Finally, we'll invite the group to use their knowledge of probability to explore whether there are any strategies that a blind person could use to increase their chances of picking a matching pair of socks.
Hannah McCarthy works for Education City, a leading supplier of e-learning software for schools and families in the UK and US. Education City offers comprehensive curriculum-based resources for teachers of Key Stage 1 Maths, together with fun maths games for kids to enjoy at home.
|
|
On the Counterfeit Coins Problem $114.71 The counterfeit coins problem is a wellknown and important one in combinatorial search theory. The problem may be simply described as that to spend the least number of weighings by a balance to find all the counterfeit coins in a set of coins. With the fascinating and interesting features, and for which there have been found some important applications to the other branches of sciences, it has been an active research topic. In this book there are included the authors main work on this topic, in the chapters 2, 3 and 4 we have presented our results for its three versions, that is the version of the number of fakes is not known beforehand, the version of multisets and the version the number of fakes is known in a range respectively. In the end of the book are four appendices including most of algorithms appeared in chapters 2,3 and 4 respectively. Author: Li, AnPing Binding Type: Paperback Number of Pages: 92 Publication Date: 2009/09/01 Language: English Dimensions: 5.98 x 9.01 x 0.22 inches |
|
|
No Problem $10 No Problem |
|
|
Coins $22.98 Coins is a magazine for coin collectors. Each issue has a full-color exploration of coin history, pricing guides for coin and paper money, and industry news. Special features of this magazine subscription include helpful guides for the beginner and serious collectors, coin bargains, inspiring letters from collectors, market analysis, and tips from the pros. |
|
|
Coins And Crosses $9.99 Coins And Crosses |
|
|
Three Coins: Cold Night $29.54 Sam the main character finds that he has a problem of being left behind by the women in his life. At a very early age his mother dies and leaves him and his father. When he graduates from high school he loses his only girl friend. Both of these events are devastating to him. But it only in college that he loses the love of his life to circumstances beyond his control. He runs away to U. S. Army for a stay before returning and marrying. Later he loses the fourth female from his life and appears completely lost. Then he returns to the town of Roelston for a funeral of a person he didnt really care about and his ventures goes on. This is an exciting tale of the life of Sam Riggs and his struggles to find happiness. Author: Springer, Tom/ Tom Springer, Springer Binding Type: Paperback Number of Pages: 220 Publication Date: 2006/02/01 Language: English Dimensions: 9.00 x 6.00 x 0.50 inches |
|
|
Problem $10 Problem - Karpina |
|
|
The Coins $18.8 Toby Franks as a young boy confronts his fear of the unknown and while doing this discovers a magical treasure that only he can unlock its secrets. He now possesses the power to choose his own destiny, but does it come with a price? Author: The Jajliardo Family/ The Jajliardo Family, Jajliardo Family Binding Type: Paperback Number of Pages: 72 Publication Date: 2004/08/01 Language: English Dimensions: 7.92 x 5.00 x 0.21 inches |
|
|
Stack of Coins $24.99 Stack of Coins - Photographic Print |
|
|
Medals and Coins $49.99 Medals and Coins - Giclee Print |
|
|
Coins of Mexico $24.99 Coins of Mexico - Premium Poster |
|
|
Chinese coins $19.99 Astock Chinese coins - Photographic Print |
|
|
The Coin Exchange Problem by Leher, Eli [Paperback] $103.56 Suppose our monetary system used only coins of the values 5 and 8. Which bills could we exchange using only these coins? How many sums are impossible to get? More generally, let a,b,...,n be natural numbers (the values of the coins). The set of all natural combinations of these numbers is a numerical semigroup. Our goal is to determine the structure of this semigroup. This question, known as the coin exchange problem or the Frobenius problem, captured the imagination of many mathematicians ever since it was first proposed by Sylvester in 1884. If we use only 2 kinds of coins, the answer is quite simple, but the case of 3 or more turns out to be much more complicated and interesting. This book presents the problem in a clear and vivid way, and shows an ingenious simple method to solve it. The main parameters of the problem, including the Frobenius number and genus, are explained and discussed. Finally, the book presents the surprising link between numerical semigroups and cyclotomic polynomials. The subject, as well as the clever solution and clear presentation, make this book a delight to anyone interested in mathematics, professionals and amateurs alike. Author: Leher, Eli Binding Type: Paperback Number of Pages: 92 Publication Date: 2009/04/01 Language: English Dimensions: 9.00 x 6.00 x 0.22 inches |
|
|
A Problem $3.99 "A Problem" by Henry James is a classic work of literature that can be enjoyed by all. Download "A Problem" and enjoy another quality Digireads.com publication. |
|
|
Coins and Bills $24.99 H. Armstrong Roberts Coins and Bills - Photographic Print |
|
|
Hands With Coins $24.99 George Marks Hands With Coins - Photographic Print |
|
|
Three Coins $29.99 Lisa Ridgers Three Coins - Art Print |
|
|
Necklace with Gold Coins $8.97 Features a gold coins necklace. |
|
|
Pirate Gold Coins $1.97 Includes twelve gold coins. |
|
|
Dancers Necklace with Coins and Mirrors $29.99 Dancers Necklace with Coins and Mirrors |
|
|
Gold Coins - Set of 30 $1.99 Gold Coins - Set of 30 |
|
|
Three Coins In The Fountain $6.99 Three Coins In The Fountain |
|
|
Coins Flannelboard Set $28.35 Coins Flannelboard Set |
|
|
Worldwide Coins $21.95 WorldWide Coins will provide timely updates about newly released coins, historical overviews of past coinages, where to find desirable coins and strategies for different approaches to collecting - whether by specific country, various topics depicted on coins, or by metallic content. <br /> |
|
|
Licorice Coins $29.95 Licorice Coins and in a very nice plastic container. Cash in your these tasty licorice coins into your taste buds. If you love licorice than this is the treat for you! |