Fair game, or not?

Probability Level 2

There are 2 friends, Illir and Alex who flip a random coin to win a bet made for some Euros. After flipping the coin for the bet, Alex tests the coin and says without lying:

-The coin is not fair, you had 70 70 p e r c e n t percent of chance to win, that means the bet was not fair! Give my Euros back!

Illir replies: - Irrelevant of what probability the coin has to show the possible result, this game is fair.

What is your opinion?

Note: They did not know the probability of the coin when the bet was finished.

Alex is right, the game is not fair because he had low probability to win. Illir is right, probability to win the bet is 1/2. Not enough info to determine.

Nikolas Кraj by Nikolas Кraj , 16, Albania

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2 solutions

Zhong Si Wei
Apr 10, 2019

There is 50-50 chance for each player to choose whether they would win if the coin flipped heads or tails, and therefore a 50-50 chance of having the 70% chance of winning. Its like their coin flip was actually the decison of which side of the coin will win instead of the coin tosses itself

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Nikolas Кraj
Mar 26, 2019

Well, with the tips it is easy to understand. We know that: Probability is from 0 (impossible) to 1 (Absolute). They flipped the coin without knowing where it is more possible to give a result. Now we say that here ( you can make an axis for this demonstration ):

  • The probability for i l l i r illir to have a coin that gives him more chance to win is from 50.00....1 p e r c e n t t o 100 p e r c e n t 50.00....1 percent to 100 percent

  • For i l l i r illir to have a more chance of loss ( or for A l e x Alex to win ) is: 49.999 p e r c e n t t o 0 p e r c e n t 49.999 percent to 0 percent . So it seems that they have equal probability for the coin to be a bias that favors them. The 70 p e r c e n t 70 percent is irrelevant in this case, just like illir said.

  • Tip : Suppose that the coin is fair which i left that out. If the coin was fair ,well, fair is the game and the coin! : ) :)

    The important part in this problem is the scene of flipping the coin. To avoid confusion: Try it yourself with a coin ( which naturally some coins usually are not homogeneous ( fair )) and say : What is the chance that this random coin can make heads a favorable result ?

0 Helpful 2 Interesting 0 Brilliant 2 Confused

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