At a county fair there is a spinner game with 10 sectors: 2 red sectors, 2 green sectors, 3 blue sectors, and 3 yellow sectors. If the spinner lands on a red sector, the player wins 3 tokens. If the spinner lands on a green sector, the player wins 5 tokens. If the spinner lands on any other sector, the player loses 2 tokens.

Is this game fair for the player and how much will the player win or lose on an average over time?

Question

Mathematics

Bogey

5 July, 06:31

At a county fair there is a spinner game with 10 sectors: 2 red sectors, 2 green sectors, 3 blue sectors, and 3 yellow sectors. If the spinner lands on a red sector, the player wins 3 tokens. If the spinner lands on a green sector, the player wins 5 tokens. If the spinner lands on any other sector, the player loses 2 tokens.

Is this game fair for the player and how much will the player win or lose on an average over time?

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Answers (1)

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Elias Hartman · Answer 1

Let the token profit be X. For a win, the profit is 2 tokens. For a loss, the profit is - 3 tokens. The probability of a win is 212 + 212 + 212 = 612 = 12 the probability of a loss is 612 = 12 Setting up a probability distribution variable gives: E (X) = (-3 * 12) + (2 * 12) = - 1 12 + 1 = - 12 token Therefore, on average, the player would expect to lose a half a token per game.