Batch 2 - Class 85 - Game of SKUNK (Probability)

• You have three color paints - red, white and blue. You want to color every point in a plane using one of these colors. However, on any line in that plane, exactly two colors must appear.

  Answer: Use base as first color, draw a cross with second color (infinite lines), and then on the intersection of the cross, use the third color to color the intersection point.
• (Expii) After a deep hundred year slumber, Ant the ant wakes up in an unfamiliar, large, dark square forest. Ant is unaware of its exact location or direction, but it does know that its starting point is exactly 10 meters away from the nearest straight edge. What is the shortest distance Ant must travel to guarantee escape from the forest? Round your answer, in meters, to the nearest hundredth.

  Answer: Not really sure - let kids describe the best solutions they have been able to come up with

• Ask kids about some of the decisions they made today, and how they made it

  Coming to the math circle class?
• Other decisions that they make, on whether they should do something or not. These are choices, but often influenced by chances of whether something might happen or not. How do we estimate chance in these scenarios?
• The connection between choice and chance provides the practical link from probability - Game of SKUNK provides that - We have done the Game of Pig before - how many people remember that?
• Quick revision of probability - ask kids how to determine probability of a certain event

  Like toss of coinLike roll of dice

• Rules of Skunk - Each letter of SKUNK represents a different round of the game; play begins with the "S" column and continue through the "K" column. The object of the game is to accumulate greatest points over five rounds. Rules:

  At beginning of each round, every player stands. Then, a pair of dice is rolledA player gets the total of the dice and records it in his or her column, unless a "1" comes up, in which case play is over for that round and all the player's points in that column are wiped outIf "double 1" comes up, all points accumulated in prior column are also wiped outIf "1" doesn't occur, the player may choose to continue standing and try for more points, or to stop and sit, in which case they get to keep what they have accumulated.If "1" or "double 1" comes on the first roll of a round, that round is over and all players bear the consequences
• Try a practice game. At end, ask students what strategies they are trying. Try another practice game, and see how students are changing their strategy
• What is the chance and what is the choice in this game?
• Can you think of other games which involve a mix of choice and chance?
• What are things that can happen in life mostly as choice? mostly as chance?
• How would you decide on whether to stand or sit in SKUNK?

  Since rolling a "1" is a disaster, it would be useful to know how many "good" rolls happen on an average before a "bad" roll. How can you find it out?Is this a good strategy or is there a better one?If a "1" isn't rolled, what is the average score you expect to get?Test it by rolling a pair of dice several timesAsk students to describe the following strategies"Play it safe"Risky strategyWhat kind of scores might you get on both of above?Choose a strategy (some kids may do either of the two), play few games and analyzeHow well do the results agree with the objective (safe or risky)Let students create a 5-grade rating chart. How many points would they allocate for each grade range? Why?
• Let students construct their own game that combines choice and chance (make a set of devices like dice available)

  Discuss the same for elements of choice and chance, clarity of articulation of the game rules.Play a game which most students in the class want to play 

• Two men are disputing over the liquid contents of a barrel. What is the particilar liquid in the barrel is impossible to say, so lets just call it water. One man says that the barrel is more than half full, the other insist is less. What is their easiest way of settling the point? There are no measures, and indeed no measuring required. Just some simple common sense!