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| The Dice Game (Posted on 2005-11-04) |
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In a game show, there is a certain game in which there are four hidden digits. There are no numbers greater than six among them, and no zeros.
You roll a die and then guess if the first digit is higher or lower than what you rolled. (If the die you rolled is equal to the first digit, you win no matter what you said.) You then roll and guess for each of the other three digits.
If you use the best strategy each time when saying "higher" or "lower", what is the chance you will get all four right and win? (Keep in mind you have no idea what the 4 digit number is.)
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Submitted by Gamer
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Rating: 3.6667 (3 votes)
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Solution:
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(Hide)
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The best strategy is to say higher with 1, 2, and 3, and lower with 4, 5, and 6.
So you have a 6/6 chance of winning on that digit if it's a 1 or 6, a 5/6 chance of winning on that digit if it's a 2 or a 5, and a 4/6 chance of winning on that digit if it's a 3 or a 4. This means you have a 5/6 chance of getting each roll right, so for 4 rolls, that is 625/1296 probability of winning. This means the odds are slightly against you. |
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