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Bar Room Toss

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #16891 Fun: (2.55) Difficulty: (1.75) Category: Probability Submitted By: jimbo Corrected By: samm

You are out one night having a few milkshakes when a shadowy figure approaches you. "Wanna play a game?" he inquires. "I'll toss two coins and look at them. If they are both tails then I'll show you both and we'll flip again. On the other hand, if they are not both tails, this is how we'll play. I'll slide one coin across to you. It has to be a head or a tail right? I'll give you \$3 if it's a head and you give me \$2 if it's a tail. Wanna play?"
Would you play with this stranger and if you decide yes, who will win or is it a fair game?

If you play you will lose. Outcomes are TT (no play) HH HT or TH. In the last 3 cases the stranger will keep a head, sliding you a tail on two occasions and a head on one occasion. He will win twice as often as you. He will win \$4 to your \$3 so in the long run you will lose.
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