Johnny and Sally sit at a table in their dining room. Sally tells Johnny to leave the room while she prepares a game. Sally randomly selects three cards from a regular deck of cards (half black, half red) and places them face down on the table. She yells at Johnny to reenter and tells him that he gets to flip two of the three cards over. If two are of the same color, Johnny wins $2. If they are different colors, Sally wins $1.(adsbygoogle = window.adsbygoogle || []).push({});

Johnny's viewpoint: It's a great deal because I have a 50% chance of winning $2 and 50% chance of losing $1. Why does he think this? The first card color he flips over is of no difference. The second card he flips has a 50% chance of being either red or black, thus 50% chance of matching the first color.

Sally's viewpoint: It's a great deal because Johnny only has 33% chance of winning so theoretically I should pay him $3 if he wins. Why does she think this? Since three cards exist, the odds of flipping over two of the same color are 1 out of 3.

Question: Who is right? Who will win? Are they somehow both right?

Thanks for the help.

**Physics Forums - The Fusion of Science and Community**

# Different Probablities Same Situation?

Have something to add?

- Similar discussions for: Different Probablities Same Situation?

Loading...

**Physics Forums - The Fusion of Science and Community**