Die roll probablility

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eninxis

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Feb 22, 2016
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Hello,

First of all, I apologize for putting you trough my bad english !
I am learning to code and trying to develop a software just for sake of learning.. I have some problems with probability math, I hope someone would enjoy to solve this:

1. If I had a die with 7 faces and every time I roll this die and number from 1 to 7 (for example "3")comes up I would mark that face/number and I would need to roll anything but 3 to continue the game. If the same face came again the game would be over. What is the probability to roll the die and to avoid hitting the same number for 6 times in row, and mark all the faces without hitting them again . Not from 1 to 7 , but in random order.

2. What are probabilities for each roll to be successful. For example if I roll "2" and mark it , my chance to hit same number and lose the game is 1/7? Or is it less, since probability to hit same number twice in row might be lower than hit some other number? So is it 1/7 after all?

Thank you, and sorry for probably (ba dum tss)bad english..
 
eninxis said:
Hello,

First of all, I apologize for putting you trough my bad english !
I am learning to code and trying to develop a software just for sake of learning.. I have some problems with probability math, I hope someone would enjoy to solve this:

1. If I had a die with 7 faces and every time I roll this die and number from 1 to 7 (for example "3")comes up I would mark that face/number and I would need to roll anything but 3 to continue the game. If the same face came again the game would be over. What is the probability to roll the die and to avoid hitting the same number for 6 times in row, and mark all the faces without hitting them again . Not from 1 to 7 , but in random order.

2. What are probabilities for each roll to be successful. For example if I roll "2" and mark it , my chance to hit same number and lose the game is 1/7? Or is it less, since probability to hit same number twice in row might be lower than hit some other number? So is it 1/7 after all?

Thank you, and sorry for probably (ba dum tss)bad english..
Click to expand...
I think what you are saying is you want all the numbers (sides of the die) but don't get two of the same numbers in a row, so lets work a simple example. for a 4 sided die (1, 2, 3, 4) we want to roll the die to get all four numbers without getting any two of the same numbers in a row, i.e. 1, 2, 3, 2, 1, 3, 4 would 'win' but 1, 2, 3, 2, 1, 3, 3 would 'lose'. Is that correct?

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Hint: A nice primer for computing combinations (order doesn't matter) and permutations (order does matter) is
https://www.mathsisfun.com/combinatorics/combinations-permutations.html
 
eninxis said:
First of all, I apologize for putting you trough my bad english !
I am learning to code and trying to develop a software just for sake of learning.. I have some problems with probability math, I hope someone would enjoy to solve this:

1. If I had a die with 7 faces and every time I roll this die and number from 1 to 7 (for example "3")comes up I would mark that face/number and I would need to roll anything but 3 to continue the game. If the same face came again the game would be over. What is the probability to roll the die and to avoid hitting the same number for 6 times in row, and mark all the faces without hitting them again . Not from 1 to 7 , but in random order.

2. What are probabilities for each roll to be successful. For example if I roll "2" and mark it , my chance to hit same number and lose the game is 1/7? Or is it less, since probability to hit same number twice in row might be lower than hit some other number? So is it 1/7 after all?
Click to expand...
One small point: It is impossible to have a fair seven sided die. Look at this. Also see the variants.

You could have a "popcorn sort" of device as used in national lotteries. With seven numbered ping-pong balls.
 
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