Finding 01 or 00 [duplicate] The Next CEO of Stack OverflowConsecutive Tail-Tail or Tail-HeadHow does one calculate the expected number of coin flips for this game to last?Probability of winning a gameFinding probability that a person gets $7$ when rolling a pair of diceGambling device: What's my probability to win at 5 dollars before going bankrupt?Probability of a team winning the series?problem 436 - project eulerProbability of a team winning a tournamentProbability question: Gambler's problemWhat is the probability of throwing 4 and then winning in craps?Consecutive Tail-Tail or Tail-Head
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Finding 01 or 00 [duplicate]
The Next CEO of Stack OverflowConsecutive Tail-Tail or Tail-HeadHow does one calculate the expected number of coin flips for this game to last?Probability of winning a gameFinding probability that a person gets $7$ when rolling a pair of diceGambling device: What's my probability to win at 5 dollars before going bankrupt?Probability of a team winning the series?problem 436 - project eulerProbability of a team winning a tournamentProbability question: Gambler's problemWhat is the probability of throwing 4 and then winning in craps?Consecutive Tail-Tail or Tail-Head
$begingroup$
This question already has an answer here:
Consecutive Tail-Tail or Tail-Head
1 answer
A and B play a bit game. Unbiased bit generator is generating 0 or 1 repeatedly until one of the following happens.
The bit patterns to '00' (i.e., a 0 is immediately followed by a 0) for the first time. In this case A wins.
The bit patterns to '01' (i.e., a 0 is immediately followed by a 1) for the first time. In this case B wins.
Who has more probability of winning the game?
I am getting both probability to be the same. Can anyone help me out how to approach this question?
probability
asked Mar 20 at 8:42
Nishant RajNishant Raj
61
$endgroup$
marked as duplicate by Arthur, John Omielan, Jaap Scherphuis, Parcly Taxel, Lee David Chung Lin Mar 21 at 1:00
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Consecutive Tail-Tail or Tail-Head
1 answer
A and B play a bit game. Unbiased bit generator is generating 0 or 1 repeatedly until one of the following happens.
The bit patterns to '00' (i.e., a 0 is immediately followed by a 0) for the first time. In this case A wins.
The bit patterns to '01' (i.e., a 0 is immediately followed by a 1) for the first time. In this case B wins.
Who has more probability of winning the game?
I am getting both probability to be the same. Can anyone help me out how to approach this question?
probability
asked Mar 20 at 8:42
Nishant RajNishant Raj
61
$endgroup$
marked as duplicate by Arthur, John Omielan, Jaap Scherphuis, Parcly Taxel, Lee David Chung Lin Mar 21 at 1:00
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
2
$begingroup$
The probabilities are indeed the same. Nothing really happens until the first $0$ and then the next bit determines the winner with equal probabilities
$endgroup$
– Henry
Mar 20 at 8:44
add a comment |
$begingroup$
This question already has an answer here:
Consecutive Tail-Tail or Tail-Head
1 answer
A and B play a bit game. Unbiased bit generator is generating 0 or 1 repeatedly until one of the following happens.
The bit patterns to '00' (i.e., a 0 is immediately followed by a 0) for the first time. In this case A wins.
The bit patterns to '01' (i.e., a 0 is immediately followed by a 1) for the first time. In this case B wins.
Who has more probability of winning the game?
I am getting both probability to be the same. Can anyone help me out how to approach this question?
probability
asked Mar 20 at 8:42
Nishant RajNishant Raj
61
$endgroup$
This question already has an answer here:
Consecutive Tail-Tail or Tail-Head
1 answer
A and B play a bit game. Unbiased bit generator is generating 0 or 1 repeatedly until one of the following happens.
The bit patterns to '00' (i.e., a 0 is immediately followed by a 0) for the first time. In this case A wins.
The bit patterns to '01' (i.e., a 0 is immediately followed by a 1) for the first time. In this case B wins.
Who has more probability of winning the game?
I am getting both probability to be the same. Can anyone help me out how to approach this question?
This question already has an answer here:
Consecutive Tail-Tail or Tail-Head
1 answer
probability
probability
asked Mar 20 at 8:42
Nishant RajNishant Raj
61
asked Mar 20 at 8:42
Nishant RajNishant Raj
61
asked Mar 20 at 8:42
Nishant RajNishant Raj
61
asked Mar 20 at 8:42
Nishant RajNishant Raj
61
asked Mar 20 at 8:42
Nishant RajNishant Raj
61
61
marked as duplicate by Arthur, John Omielan, Jaap Scherphuis, Parcly Taxel, Lee David Chung Lin Mar 21 at 1:00
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Arthur, John Omielan, Jaap Scherphuis, Parcly Taxel, Lee David Chung Lin Mar 21 at 1:00
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
2
$begingroup$
The probabilities are indeed the same. Nothing really happens until the first $0$ and then the next bit determines the winner with equal probabilities
$endgroup$
– Henry
Mar 20 at 8:44
add a comment |
2
$begingroup$
The probabilities are indeed the same. Nothing really happens until the first $0$ and then the next bit determines the winner with equal probabilities
$endgroup$
– Henry
Mar 20 at 8:44
2
2
$begingroup$
The probabilities are indeed the same. Nothing really happens until the first $0$ and then the next bit determines the winner with equal probabilities
$endgroup$
– Henry
Mar 20 at 8:44
$begingroup$
The probabilities are indeed the same. Nothing really happens until the first $0$ and then the next bit determines the winner with equal probabilities
$endgroup$
– Henry
Mar 20 at 8:44
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The first $0$ is followed by a $0$ or a $1$ equiprobably and the game is over.
answered Mar 20 at 8:45
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
In this scenario, note that once the first $0$ is generated, then the next number generated determines the victor of the game. The only thing that could happen prior to the first $0$ is some finite sequence of $1$'s which wouldn't help anyone, so we don't care about anything until that first $0$.
In which case the conclusion is clear - there's a $1/2$ probability to get a $0$ on the succeeding digit, and $1/2$ for a $1$.
Thus, the probabilities of each winning are the same.
answered Mar 20 at 8:45
Eevee TrainerEevee Trainer
9,23631640
$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The first $0$ is followed by a $0$ or a $1$ equiprobably and the game is over.
answered Mar 20 at 8:45
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
The first $0$ is followed by a $0$ or a $1$ equiprobably and the game is over.
answered Mar 20 at 8:45
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
The first $0$ is followed by a $0$ or a $1$ equiprobably and the game is over.
answered Mar 20 at 8:45
Yves DaoustYves Daoust
131k676229
$endgroup$
The first $0$ is followed by a $0$ or a $1$ equiprobably and the game is over.
answered Mar 20 at 8:45
Yves DaoustYves Daoust
131k676229
answered Mar 20 at 8:45
Yves DaoustYves Daoust
131k676229
answered Mar 20 at 8:45
Yves DaoustYves Daoust
131k676229
answered Mar 20 at 8:45
Yves DaoustYves Daoust
131k676229
131k676229
add a comment |
add a comment |
$begingroup$
In this scenario, note that once the first $0$ is generated, then the next number generated determines the victor of the game. The only thing that could happen prior to the first $0$ is some finite sequence of $1$'s which wouldn't help anyone, so we don't care about anything until that first $0$.
In which case the conclusion is clear - there's a $1/2$ probability to get a $0$ on the succeeding digit, and $1/2$ for a $1$.
Thus, the probabilities of each winning are the same.
answered Mar 20 at 8:45
Eevee TrainerEevee Trainer
9,23631640
$endgroup$
add a comment |
$begingroup$
In this scenario, note that once the first $0$ is generated, then the next number generated determines the victor of the game. The only thing that could happen prior to the first $0$ is some finite sequence of $1$'s which wouldn't help anyone, so we don't care about anything until that first $0$.
In which case the conclusion is clear - there's a $1/2$ probability to get a $0$ on the succeeding digit, and $1/2$ for a $1$.
Thus, the probabilities of each winning are the same.
answered Mar 20 at 8:45
Eevee TrainerEevee Trainer
9,23631640
$endgroup$
add a comment |
$begingroup$
In this scenario, note that once the first $0$ is generated, then the next number generated determines the victor of the game. The only thing that could happen prior to the first $0$ is some finite sequence of $1$'s which wouldn't help anyone, so we don't care about anything until that first $0$.
In which case the conclusion is clear - there's a $1/2$ probability to get a $0$ on the succeeding digit, and $1/2$ for a $1$.
Thus, the probabilities of each winning are the same.
answered Mar 20 at 8:45
Eevee TrainerEevee Trainer
9,23631640
$endgroup$
In this scenario, note that once the first $0$ is generated, then the next number generated determines the victor of the game. The only thing that could happen prior to the first $0$ is some finite sequence of $1$'s which wouldn't help anyone, so we don't care about anything until that first $0$.
In which case the conclusion is clear - there's a $1/2$ probability to get a $0$ on the succeeding digit, and $1/2$ for a $1$.
Thus, the probabilities of each winning are the same.
answered Mar 20 at 8:45
Eevee TrainerEevee Trainer
9,23631640
answered Mar 20 at 8:45
Eevee TrainerEevee Trainer
9,23631640
answered Mar 20 at 8:45
Eevee TrainerEevee Trainer
9,23631640
answered Mar 20 at 8:45
Eevee TrainerEevee Trainer
9,23631640
9,23631640
add a comment |
add a comment |
2
$begingroup$
The probabilities are indeed the same. Nothing really happens until the first $0$ and then the next bit determines the winner with equal probabilities
$endgroup$
– Henry
Mar 20 at 8:44