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### #1

Posted 08 January 2008 - 09:34 PM

If you throw a dice twice the cance of getting six is 2/6

If you throw a dice three times the cance of getting six is 3/6

If you throw a dice four times the cance of getting six is 4/6

If you throw a dice five times the cance of getting six is 5/6

Does this mean that if you throw a dice 6 times you are garantied 6?

Of course it doesn't but how come theareticly the chance is 100% when practicly it isn't.

### #2

Posted 08 January 2008 - 10:06 PM

If you throw a dice once the cance of getting six is 1/6

If you throw a dice twice the cance of getting six is 2/6

If you throw a dice three times the cance of getting six is 3/6

If you throw a dice four times the cance of getting six is 4/6

If you throw a dice five times the cance of getting six is 5/6

Does this mean that if you throw a dice 6 times you are garantied 6?

Of course it doesn't but how come theareticly the chance is 100% when practicly it isn't.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #3

Posted 08 January 2008 - 10:09 PM

Your odds aren't quite right.If you throw a dice once the cance of getting six is 1/6

If you throw a dice twice the cance of getting six is 2/6

If you throw a dice three times the cance of getting six is 3/6

If you throw a dice four times the cance of getting six is 4/6

If you throw a dice five times the cance of getting six is 5/6

Does this mean that if you throw a dice 6 times you are garantied 6?

Of course it doesn't but how come theareticly the chance is 100% when practicly it isn't.

If you throw a die (btw, singular is 'die', plural is 'dice') you have a one in six chance of getting a specified number, e.g. six. That means you have five chances in six of

*not*getting a six.

In two dice rolls, your chances of

*not*getting a six are 5/6 for the first roll and 5/6 for the second roll, giving you total odds of (5/6) * (5/6), or 25/36, of

*not*getting a six. Thus, your odds for getting at least one six are one (100% odds) minus the odds of

*not*getting at least one six: 1 - 25/36, or 11/36. Note that this is slightly

*smaller*than 2/6 (= 12/36), as you had said above.

In six dice rolls, your odds of

*not*getting a six are therefore (5/6)^6, or 15625/46656, which is just a bit greater than 1/3 odds. Therefore, your odds of rolling at least one six are one minus this amount, which as a percent is 66.5%.

### #4

Posted 08 January 2008 - 10:12 PM

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