Congratulations to all of you who sent in a correct answer to this problem. There were too many of you to name all of you here, but well done! The first correct answer was sent in by Natasha and Nataneil:

Derek's chance is 1 in 6 whereas Tania's chance is 3 in 6 which gives Tania a bigger chance to win.

This is because there are 6 numbers on a die and Derek has only chosen 1, and because Tania has chosen 3 she has a bigger probability to win!!!

To make the game fair one person should have all the odd numbers and the other person have all the even numbers.

I wonder if there are some other ways of playing a fair game?