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In the game of Ludo, a player has to throw one die and move a selected token based on the number shown on the die. If a six is shown, the player takes an additional turn in the same round and the number of moves is the number shown the second time and the previous six. If a six appears for the second time, the process is repeated with the move depending on the number shown and the previous throws. If a six appears for the third time, the turn of the player ends without moving the token.

Determine the sample space of one such throw and determine the probability for each event.

So if I understand this correctly, the outcomes would be 1 to 5, only one roll.

If a 6 is rolled, it is 6 + (1 to 5) = 7 to 11 and 2 rolls.

If two 6's are rolled, it is 12 + (1 to 6) = 13-17 and 3 rolls.

So the number of spaces moved is 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,`8.

The numbers 6 and 12 are not included because the die has to be thrown again.

The chance of 1 to 5 is 1/6.

The chance of 7-11 is 1/6 of the 1/6 chance of getting the first roll as a 6,

and that is 1/36.

The chance of 13-18 is each 1/6 chance of the 1/36 chance of getting that far,

so it is 1/216 each.

This makes the chances as follows

1 1/6

2 1/6

3 1/6

4 1/6

5 1/6

7 1/36

8 1/36

9 1/36

10 1/36

11 1/36

13 1/216

14 1/216

15 1/216

16 1/216

17 1/216

18 1/216

Now to make sure this is correct, add up the chances and the result should be 1.

Note that the last 6 possibilities added together are 6(1/216) = 1/36.

When the chances of 7-11 are added together and the last one included,

we get 5/36 + 1/36 = 6/36 = 1/6.

When the chances of 1-5 are added with this added on, we get 5/6 + 1/6 = 1.

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