Question

In playing Monopoly, rolling doubles three times in a row sends you to jail. If you roll the dice 100 times over the course of a game, what is the probability that you will have rolled doubles, at any point, exactly three times?

Answer 1

You have 5/6 , or 83.333% chance of not throwing doubles.

You have a 5/36, or 13.88888% chance of throwing doubles once, then not throwing doubles.

You have a 5/216, or 2.31% chance of throwing doubles twice, then not throwing doubles.

You have a 1/216, or 0.46% chance of throwing doubles 3 times in a row.

Once you throw one die, the odds of the other one matching are 1/6. That's what the probabilities are based on, or, there are 36 possible combinations, and 6 of them are doubles, same thing.

If this is not Monopoly, and you allowed to throw the dice a 4th time if the first three are doubles, then 1/1296 times you will throw at least one more double, so you would not have exactly 3 doubles. And 5/1296 times you will throw not doubles after 3 doubles, so then, the answer for exactly three doubles would be 5/1296, which is 0.39%.

Answer 2

medal????