Do your own experiments using number cards to play the games and pick 2 cards at random each time.

In Game A an envelope or bag contains balls, or cards, numbered 2, 3, 4, 5 and 6.  Pick out two balls or cards at random. If the total is even you win. If it is odd you lose. Are you equally likely to win or to lose (a fair game)?

Games B, C and D use the numbers shown and the rules are the same.

Which set of balls would you choose to give yourself the best chance of winning?

Can you find a different set of numbers to make this a fair game?

Put 3 red cards and 6 blue cards in a bag. Each player must choose whether to to be a ‘same’ player who wins when the 2 cards drawn are the same colour, or a ‘different’ player who wins when they are different.  Take turns to pick two cards at random, first one then another without replacing the first card, and score a point (or not) depending on whether the cards are the same colour. Put the cards back and shake the bag. Repeat until one of the players has won 5 points.

Is this a fair game? Would it still be a fair game if you put different numbers of cards in the bag?

What do you notice about the Odds and Evens games and the Red Blue games?

Click here for the ODDS AND EVENS GAMES worksheet.

Click here for the ODDS AND EVENS GAMES Inclusion and Home Learning Guide.

Click here for Notes for Teachers for years 9 to 11.

Click here for Proof Sorting Activity for Years 12 & 13

This problem is adapted from the NRICH task Odds and Evens with permission of the University of Cambridge. All rights reserved. You can play the games using the NRICH interactive computer simulations.

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