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Question
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.

Volunteer

#### Scott A Wilson

##### Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

##### Experience

Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.