Probability Game with Dice
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I keep throwing dice until I have seen 8 consecutive fives, after which I stop. What is the probability that under this scheme I will at any point have seen 10 consecutive sixes?
Is there any way to solve the question without using Markov Chains or doing tedious calculations, maybe by using clever arguments?
probability dice
asked Nov 23 at 10:56
anmol porwal
1011
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show 4 more comments
up vote
-1
down vote
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I keep throwing dice until I have seen 8 consecutive fives, after which I stop. What is the probability that under this scheme I will at any point have seen 10 consecutive sixes?
Is there any way to solve the question without using Markov Chains or doing tedious calculations, maybe by using clever arguments?
probability dice
asked Nov 23 at 10:56
anmol porwal
1011
1
What is the probability getting a 6, and then another 6? Can you extrapolate this to your case?
– Patricio
Nov 23 at 10:58
This is fairly routine, if a bit tedious, using states. Use the states to store information regarding the then current consecutive string, if any.
– lulu
Nov 23 at 11:02
@lulu I understand that it can be done using markov chains, but I was wondering if there is a simpler way of doing it?
– anmol porwal
Nov 23 at 11:29
I doubt it. Well, it's easy to simulate if you don't mind a numerical result.
– lulu
Nov 23 at 11:32
It was asked in one of the tests as an MCQ and was expected to be done in much less time without using calculators etc., so I thought maybe there was a way.
– anmol porwal
Nov 23 at 11:39
|
show 4 more comments
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I keep throwing dice until I have seen 8 consecutive fives, after which I stop. What is the probability that under this scheme I will at any point have seen 10 consecutive sixes?
Is there any way to solve the question without using Markov Chains or doing tedious calculations, maybe by using clever arguments?
probability dice
asked Nov 23 at 10:56
anmol porwal
1011
I keep throwing dice until I have seen 8 consecutive fives, after which I stop. What is the probability that under this scheme I will at any point have seen 10 consecutive sixes?
Is there any way to solve the question without using Markov Chains or doing tedious calculations, maybe by using clever arguments?
probability dice
probability dice
asked Nov 23 at 10:56
anmol porwal
1011
asked Nov 23 at 10:56
anmol porwal
1011
edited Nov 23 at 11:50
asked Nov 23 at 10:56
anmol porwal
1011
asked Nov 23 at 10:56
anmol porwal
1011
asked Nov 23 at 10:56
anmol porwal
1011
1011
1
What is the probability getting a 6, and then another 6? Can you extrapolate this to your case?
– Patricio
Nov 23 at 10:58
This is fairly routine, if a bit tedious, using states. Use the states to store information regarding the then current consecutive string, if any.
– lulu
Nov 23 at 11:02
@lulu I understand that it can be done using markov chains, but I was wondering if there is a simpler way of doing it?
– anmol porwal
Nov 23 at 11:29
I doubt it. Well, it's easy to simulate if you don't mind a numerical result.
– lulu
Nov 23 at 11:32
It was asked in one of the tests as an MCQ and was expected to be done in much less time without using calculators etc., so I thought maybe there was a way.
– anmol porwal
Nov 23 at 11:39
|
show 4 more comments
1
What is the probability getting a 6, and then another 6? Can you extrapolate this to your case?
– Patricio
Nov 23 at 10:58
This is fairly routine, if a bit tedious, using states. Use the states to store information regarding the then current consecutive string, if any.
– lulu
Nov 23 at 11:02
@lulu I understand that it can be done using markov chains, but I was wondering if there is a simpler way of doing it?
– anmol porwal
Nov 23 at 11:29
I doubt it. Well, it's easy to simulate if you don't mind a numerical result.
– lulu
Nov 23 at 11:32
It was asked in one of the tests as an MCQ and was expected to be done in much less time without using calculators etc., so I thought maybe there was a way.
– anmol porwal
Nov 23 at 11:39
1
1
What is the probability getting a 6, and then another 6? Can you extrapolate this to your case?
– Patricio
Nov 23 at 10:58
What is the probability getting a 6, and then another 6? Can you extrapolate this to your case?
– Patricio
Nov 23 at 10:58
This is fairly routine, if a bit tedious, using states. Use the states to store information regarding the then current consecutive string, if any.
– lulu
Nov 23 at 11:02
This is fairly routine, if a bit tedious, using states. Use the states to store information regarding the then current consecutive string, if any.
– lulu
Nov 23 at 11:02
@lulu I understand that it can be done using markov chains, but I was wondering if there is a simpler way of doing it?
– anmol porwal
Nov 23 at 11:29
@lulu I understand that it can be done using markov chains, but I was wondering if there is a simpler way of doing it?
– anmol porwal
Nov 23 at 11:29
I doubt it. Well, it's easy to simulate if you don't mind a numerical result.
– lulu
Nov 23 at 11:32
I doubt it. Well, it's easy to simulate if you don't mind a numerical result.
– lulu
Nov 23 at 11:32
It was asked in one of the tests as an MCQ and was expected to be done in much less time without using calculators etc., so I thought maybe there was a way.
– anmol porwal
Nov 23 at 11:39
It was asked in one of the tests as an MCQ and was expected to be done in much less time without using calculators etc., so I thought maybe there was a way.
– anmol porwal
Nov 23 at 11:39
|
show 4 more comments
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1
What is the probability getting a 6, and then another 6? Can you extrapolate this to your case?
– Patricio
Nov 23 at 10:58
This is fairly routine, if a bit tedious, using states. Use the states to store information regarding the then current consecutive string, if any.
– lulu
Nov 23 at 11:02
@lulu I understand that it can be done using markov chains, but I was wondering if there is a simpler way of doing it?
– anmol porwal
Nov 23 at 11:29
I doubt it. Well, it's easy to simulate if you don't mind a numerical result.
– lulu
Nov 23 at 11:32
It was asked in one of the tests as an MCQ and was expected to be done in much less time without using calculators etc., so I thought maybe there was a way.
– anmol porwal
Nov 23 at 11:39