Solution: What Are Your Chances? Math Puzzle
The probability of getting a 2 is 1/36. The probability of getting a 7 is 1/6. You are six times more likely to get a 7 than to get a 2. To see why, look at this chart, which shows all the possible outcomes of throwing a pair of dice.
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die 1
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die 2
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1
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1
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1
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2
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1
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3
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1
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4
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1
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5
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1
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6
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2
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1
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2
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2
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2
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3
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2
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4
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2
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5
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2
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6
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3
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1
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3
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2
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3
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3
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3
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4
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3
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5
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3
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6
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4
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1
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4
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2
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4
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3
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4
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4
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4
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5
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4
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6
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5
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1
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5
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2
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5
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3
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5
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4
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5
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5
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5
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6
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6
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1
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6
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2
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6
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3
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6
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4
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6
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5
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6
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6
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There are 36 possible outcomes. One of these, shown in green, is a 2, that is, a 1 on each die. So the probability of getting a 2 is 1/36.
Six of the 36 possibilities, shown in red, add up to 7. So the probability of getting a 7 is 6/36 or 1/6.
In this game you throw a pair of dice. If it comes up 7, you win; if not you lose. You are pretty cautious, so you won’t play unless you have at least a 50% chance of winning. You know that if you get only one throw, your chance of winning is only 1 out of 6, so you ask for more than one throw. How many throws should you insist on to raise your chance of winning to 50% or more?
In this math puzzle we throw the dice to figure out probabilities. Special thanks to Kinapara Coulibaly, Claude Baudoin, and David Tempel for their help.