Ron and Kenneth decide to gamble. Four aces are taken from an ordinary deck of cards. The four aces are placed faced down and Kenneth is to flip 2 over cards. If both aces are of the same colour Kenneth wins 50 dollars. If not Ron will win 50 dollars.
Kenneth disagrees to this wager and requested that he wins 100 if he flips 2 of the same colour.
Is this a fair bet?
The answer is yes.
You may be wondering why it is fair for Kenneth to win 100 whereas Ron only gets 50. If we look at all the possible outcomes of flipping cards we get four possibilities. RR, RB, BR and BB. It may seem like there is a 50-50 chance of flipping the same colour but this is incorrect.
If we take another approach, if the first flipped card was red, there would be one red in the 3 unflipped cards and there would be a 1/3 chance of flipping that red. This is the same case as if the first card flipped was black. Therefore the chance of flipping two cards of the same colour is actually 1 in 3 not 50-50. Therefore it is fair for Kenneth to win double because he is half as likely to win.
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