**A coin is tossed repeatedly. If it comes up heads Pascal gets a point but if it comes up tails Fermat wins a point. The first person to win three points is the winner and receives the prize of £12.**

**Unfortunately the game had to end abruptly after three tosses of the coin. Pascal had two points and Fermat had one point. They decided to share the £12 in a ratio that matched the probability of them winning the game if it had continued.**

**How should they divide the £12?**

You may be surprised at the correct answer as it is not £8 and £4!

Tweet about this starter | Share |

Topics: Starter

How did you use this starter? Can you suggest
how teachers could present or develop this resource? Do you have any comments? It is always useful to receive
feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this

Good, achieved the results I required

Satisfactory

Didn't really capture the interest of the students

Not for me! I wouldn't use this type of activity.

Good, achieved the results I required

Satisfactory

Didn't really capture the interest of the students

Not for me! I wouldn't use this type of activity.

Previous Day | This starter is for | Next Day

The solutions to this and other Transum puzzles, exercises and activities are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

A Transum subscription also gives you access to the 'Class Admin' student management system, downloadable worksheets, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.

More Mathematics Lesson Starters

Eric Levy, United States

Thursday, November 17, 2016

"Thank you for the podcasts! I really enjoy the puzzles. This relates to the 5/29/15 podcast re: coin flipping game that was stopped before completion. The flips when stopped were two Heads and one Tail. You indicate that the options on next 2 tosses are HH, TH, HT, and TT. Since the game stops when one person reaches 3 points, wouldn't HH and HT be the same, as the second flip isn't needed? This seems to match your ultimate answer of 75% and 25%, though ... with the person with Tails only winning with TT, which is 25% chance. I get the same answer but intermediate steps differ. Am I looking at this incorrectly? Thanks!"

Transum,

Thursday, November 17, 2016

"Dear Eric, Thanks so much for your observations and you are completely correct. The only reason I chose to list the next two outcomes was to produce ‘equally likely’ outcomes making the arithmetic very slightly easier. I’m glad you enjoy the puzzles."

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world. Click here to enter your comments.

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.

## Have you read Craig's book yet?Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more... "How I wish I’d taught maths' is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL. |

## Casio Classwiz CalculatorThere is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app). As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols! This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more... |