Task Name : Pick Two Cards | Task Level : J (Year 9) | ||
Semester : 1 | Topic : Chance | VC Strand : Chance | |
Web Address : http://maths.crusoecollege.vic.edu.au/chanceJ | |||
Equipment Needed : Playing cards (one pack will do several students) | |||
Victorian Curriculum outcome : List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events. Calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’ or ‘or’. | |||
Task description : Students play “Pick Two Cards” where six cards (three black and three red) are held by the dealer. The player picks two of these (without looking). If the cards are the same colour, the player wins. If they are different colours, the dealer wins. Students play fifty times and estimate the relative probabilities of each participant winning. They then use tree diagrams to find the actual probabilities (they will find the game is weighted in favour of the dealer). Students then find examples of fair games using the construction of tree diagrams. | |||
Assessment options : Written or digital records of the tree diagrams used to show the fair games. | |||
Teacher notes: As students find fair games (and can prove this using a tree diagram), ask them to record the card ratio on the class whiteboard. This will encourage students to be more systematic in their testing and will reveal a pattern: the difference between the number of cards squared is the total number of cards, e.g. 1 red and 3 black is fair, the difference is 2 and there are 4 cards total (2 squared).
Extension: Students design a game of chance |