The 3-card Thriller game costs $3 to play and involves a 3-card deck where: • one card has red on both sides • one card has black on both sides • one card has red on one side and black on the other side. Once you pay, the host running the game draws a single card at random from the 3-card deck and shows you the colour of one of it’s sides. If you can correctly guess the colour of the other side of this card (the side you can’t see) you win $7. If you guess incorrectly you get nothing (i.e. $0, and a deep feeling of shame...). Prove that the expected value of this game is greatest when you always guess the same colour. Include a full mathematical expla- nation of all probabilities and include any references or sources.
The 3-card Thriller game costs $3 to play and involves a 3-card deck where:
• one card has red on both sides
• one card has black on both sides
• one card has red on one side and black on the other side.
Once you pay, the host running the game draws a single card at random from the 3-card deck and shows you the colour of one of it’s sides. If you can correctly guess the colour of the other side of this card (the side you can’t see) you win $7. If you guess incorrectly you get nothing (i.e. $0, and a deep feeling of shame...).
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Prove that the
expected value of this game is greatest when you always guess the same colour. Include a full mathematical expla- nation of all probabilities and include any references or sources.
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