In Game A you pick out two balls at random from a bag containing balls numbered 2, 3, 4, 5 and 6.. 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)?
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?
To do your own experiments, either use number cards to play the games and pick 2 cards at random each time.
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.