If a group of people have to choose an option, fairly, here are a few ways they could do it.
1. Take a vote. Whichever option was chosen by more people is the one that everyone will choose in the end.
2. Flip a coin. Choose which option will be heads and which will be tails. Flip the coin and whichever side comes up is the option that will be chosen.
3. Draw from a hat. Write both options on slips of paper and place into a hat or bag. Have one person blindly draw one slip of paper. Whichever option the paper has written on it that was chosen is the option chosen in the end.
Hope this helps!! :)