Mixing
Pick Balls with Unequal Probabilities
There are some balls with 4 different colors in a black box.
The ratio of A color ball is 10%, B is 20%, C is 30% and D is 40%.
The rule of this game is that you randomly pick one ball and mark the color of this ball then throw it back to the box.
The Question is:
When you already have marked 2 different color balls, what is the probability of that the next time you pick one ball is the same color with the previous 2 colors (P22), and is different with previous 2 colors (P23).
Here is what I thought:
Use Markov matrix to solve the problem, the states are AB AC AD BC BD CD ABC ABD BCD ACD, so we can build a $10 * 10$ matrix T: $$AB->AB = 0.3, AB->AC=0.0 ... AB->ABC=0.3, AB->ABD=0.4$$ etc.
calc:
$$lim_{ntoinfty} {T}^n$$
I am not sure this method is correct.
Is this a Poisson Process?
markov-chains markov-process conditional-probability poisson-process
asked Nov 21 '18 at 17:38
J.BrownJ.Brown
11
add a comment |
There are some balls with 4 different colors in a black box.
The ratio of A color ball is 10%, B is 20%, C is 30% and D is 40%.
The rule of this game is that you randomly pick one ball and mark the color of this ball then throw it back to the box.
The Question is:
When you already have marked 2 different color balls, what is the probability of that the next time you pick one ball is the same color with the previous 2 colors (P22), and is different with previous 2 colors (P23).
Here is what I thought:
Use Markov matrix to solve the problem, the states are AB AC AD BC BD CD ABC ABD BCD ACD, so we can build a $10 * 10$ matrix T: $$AB->AB = 0.3, AB->AC=0.0 ... AB->ABC=0.3, AB->ABD=0.4$$ etc.
calc:
$$lim_{ntoinfty} {T}^n$$
I am not sure this method is correct.
Is this a Poisson Process?
markov-chains markov-process conditional-probability poisson-process
asked Nov 21 '18 at 17:38
J.BrownJ.Brown
11
Please clarify the question sentence. Did you mean that the ball you are picking has the either the same color as the two previous ones or a different color than the two previously found balls?
– Mefitico
Nov 21 '18 at 17:49
Actually there are two probabilities I want to calculate. The one (P22) is that the probability of that the next time you pick one ball is the same color with the previous 2 colors, the other(P23) is that the probability of that the next time you pick one ball is different with previous 2 colors. Sorry for the misunderstanding.
– J.Brown
Nov 22 '18 at 2:11
add a comment |
There are some balls with 4 different colors in a black box.
The ratio of A color ball is 10%, B is 20%, C is 30% and D is 40%.
The rule of this game is that you randomly pick one ball and mark the color of this ball then throw it back to the box.
The Question is:
When you already have marked 2 different color balls, what is the probability of that the next time you pick one ball is the same color with the previous 2 colors (P22), and is different with previous 2 colors (P23).
Here is what I thought:
Use Markov matrix to solve the problem, the states are AB AC AD BC BD CD ABC ABD BCD ACD, so we can build a $10 * 10$ matrix T: $$AB->AB = 0.3, AB->AC=0.0 ... AB->ABC=0.3, AB->ABD=0.4$$ etc.
calc:
$$lim_{ntoinfty} {T}^n$$
I am not sure this method is correct.
Is this a Poisson Process?
markov-chains markov-process conditional-probability poisson-process
asked Nov 21 '18 at 17:38
J.BrownJ.Brown
11
There are some balls with 4 different colors in a black box.
The ratio of A color ball is 10%, B is 20%, C is 30% and D is 40%.
The rule of this game is that you randomly pick one ball and mark the color of this ball then throw it back to the box.
The Question is:
When you already have marked 2 different color balls, what is the probability of that the next time you pick one ball is the same color with the previous 2 colors (P22), and is different with previous 2 colors (P23).
Here is what I thought:
Use Markov matrix to solve the problem, the states are AB AC AD BC BD CD ABC ABD BCD ACD, so we can build a $10 * 10$ matrix T: $$AB->AB = 0.3, AB->AC=0.0 ... AB->ABC=0.3, AB->ABD=0.4$$ etc.
calc:
$$lim_{ntoinfty} {T}^n$$
I am not sure this method is correct.
Is this a Poisson Process?
markov-chains markov-process conditional-probability poisson-process
markov-chains markov-process conditional-probability poisson-process
asked Nov 21 '18 at 17:38
J.BrownJ.Brown
11
asked Nov 21 '18 at 17:38
J.BrownJ.Brown
11
edited Nov 25 '18 at 9:33
J.Brown
asked Nov 21 '18 at 17:38
J.BrownJ.Brown
11
asked Nov 21 '18 at 17:38
J.BrownJ.Brown
11
asked Nov 21 '18 at 17:38
J.BrownJ.Brown
11
11
Please clarify the question sentence. Did you mean that the ball you are picking has the either the same color as the two previous ones or a different color than the two previously found balls?
– Mefitico
Nov 21 '18 at 17:49
Actually there are two probabilities I want to calculate. The one (P22) is that the probability of that the next time you pick one ball is the same color with the previous 2 colors, the other(P23) is that the probability of that the next time you pick one ball is different with previous 2 colors. Sorry for the misunderstanding.
– J.Brown
Nov 22 '18 at 2:11
add a comment |
Please clarify the question sentence. Did you mean that the ball you are picking has the either the same color as the two previous ones or a different color than the two previously found balls?
– Mefitico
Nov 21 '18 at 17:49
Actually there are two probabilities I want to calculate. The one (P22) is that the probability of that the next time you pick one ball is the same color with the previous 2 colors, the other(P23) is that the probability of that the next time you pick one ball is different with previous 2 colors. Sorry for the misunderstanding.
– J.Brown
Nov 22 '18 at 2:11
Please clarify the question sentence. Did you mean that the ball you are picking has the either the same color as the two previous ones or a different color than the two previously found balls?
– Mefitico
Nov 21 '18 at 17:49
Please clarify the question sentence. Did you mean that the ball you are picking has the either the same color as the two previous ones or a different color than the two previously found balls?
– Mefitico
Nov 21 '18 at 17:49
Actually there are two probabilities I want to calculate. The one (P22) is that the probability of that the next time you pick one ball is the same color with the previous 2 colors, the other(P23) is that the probability of that the next time you pick one ball is different with previous 2 colors. Sorry for the misunderstanding.
– J.Brown
Nov 22 '18 at 2:11
Actually there are two probabilities I want to calculate. The one (P22) is that the probability of that the next time you pick one ball is the same color with the previous 2 colors, the other(P23) is that the probability of that the next time you pick one ball is different with previous 2 colors. Sorry for the misunderstanding.
– J.Brown
Nov 22 '18 at 2:11
add a comment |
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Please clarify the question sentence. Did you mean that the ball you are picking has the either the same color as the two previous ones or a different color than the two previously found balls?
– Mefitico
Nov 21 '18 at 17:49
Actually there are two probabilities I want to calculate. The one (P22) is that the probability of that the next time you pick one ball is the same color with the previous 2 colors, the other(P23) is that the probability of that the next time you pick one ball is different with previous 2 colors. Sorry for the misunderstanding.
– J.Brown
Nov 22 '18 at 2:11