Expected ratio of turns for complicated ball drawing game
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I am stumped once again by another expectation value question. The question is as follows.
Alice, Bob and Charles play a game. In front of the players are four urns, each containing an equal number of balls of each of six different colours (red, orange, yellow, green, blue, and purple). In a single turn, a player draws a ball at random from each urn, aiming to draw four of the same colour. The four balls are then returned to the original urns and the turn ends.
In the final turn of a particular game, Alice draws 2 green balls, 1 blue and 1 red. Bob draws 3 red balls and 1 yellow. Charles finally draws 4 blue balls and wins. What is the expected number of rounds made by each player, including the final round, relative to each other?
There is so much information I have no idea where to begin. At first I was considering calculating the expected number of turns to obtain the particular combination they finally obtained and taking the ratio, but no information is given about previous turns. I am incredibly lost — please help!
Edit: this was multiple choice, and I believe the options were:
1) Charles played 5x as many rounds as Bob, who played 4x as many as Alice
2) Charles played 20x as many rounds as Bob, who played 4x as many as Alice
3) Charles played 5x as many rounds as Bob, who played 6x as many as Alice
4) Charles played 20x as many rounds as Bob, who played 6x as many as Alice
5) None of the above
I hope this clarifies things!
probability game-theory conditional-expectation expected-value
asked Nov 23 at 4:27
user107224
378214
add a comment |
up vote
0
down vote
favorite
I am stumped once again by another expectation value question. The question is as follows.
Alice, Bob and Charles play a game. In front of the players are four urns, each containing an equal number of balls of each of six different colours (red, orange, yellow, green, blue, and purple). In a single turn, a player draws a ball at random from each urn, aiming to draw four of the same colour. The four balls are then returned to the original urns and the turn ends.
In the final turn of a particular game, Alice draws 2 green balls, 1 blue and 1 red. Bob draws 3 red balls and 1 yellow. Charles finally draws 4 blue balls and wins. What is the expected number of rounds made by each player, including the final round, relative to each other?
There is so much information I have no idea where to begin. At first I was considering calculating the expected number of turns to obtain the particular combination they finally obtained and taking the ratio, but no information is given about previous turns. I am incredibly lost — please help!
Edit: this was multiple choice, and I believe the options were:
1) Charles played 5x as many rounds as Bob, who played 4x as many as Alice
2) Charles played 20x as many rounds as Bob, who played 4x as many as Alice
3) Charles played 5x as many rounds as Bob, who played 6x as many as Alice
4) Charles played 20x as many rounds as Bob, who played 6x as many as Alice
5) None of the above
I hope this clarifies things!
probability game-theory conditional-expectation expected-value
asked Nov 23 at 4:27
user107224
378214
Hmm... It all made some sense before the words "relative to each other", after which I got lost too: how could it be that the players made different numbers of turns? I guess your best bet is just to ask whoever gave you this problem what exactly the conditions mean and what the question is.
– fedja
Nov 23 at 5:11
@fedja Hello, I’ve added options for clarity!
– user107224
Nov 23 at 8:07
Then my guess is that the intended answer is (4) (Compare the frequencies (=probabilities) of getting all 4 of one color, 3+1, and 2+1+1), but whoever formulated the problem the way it was stated was thoroughly confused about either the English language, or mathematics, or both, because the meaning conveyed has pretty much nothing to do with the meaning intended (Alice aims at exactly 2 of the same color to stop, Bob aims at exactly 3, Charles goes for all 4).
– fedja
Nov 23 at 11:31
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am stumped once again by another expectation value question. The question is as follows.
Alice, Bob and Charles play a game. In front of the players are four urns, each containing an equal number of balls of each of six different colours (red, orange, yellow, green, blue, and purple). In a single turn, a player draws a ball at random from each urn, aiming to draw four of the same colour. The four balls are then returned to the original urns and the turn ends.
In the final turn of a particular game, Alice draws 2 green balls, 1 blue and 1 red. Bob draws 3 red balls and 1 yellow. Charles finally draws 4 blue balls and wins. What is the expected number of rounds made by each player, including the final round, relative to each other?
There is so much information I have no idea where to begin. At first I was considering calculating the expected number of turns to obtain the particular combination they finally obtained and taking the ratio, but no information is given about previous turns. I am incredibly lost — please help!
Edit: this was multiple choice, and I believe the options were:
1) Charles played 5x as many rounds as Bob, who played 4x as many as Alice
2) Charles played 20x as many rounds as Bob, who played 4x as many as Alice
3) Charles played 5x as many rounds as Bob, who played 6x as many as Alice
4) Charles played 20x as many rounds as Bob, who played 6x as many as Alice
5) None of the above
I hope this clarifies things!
probability game-theory conditional-expectation expected-value
asked Nov 23 at 4:27
user107224
378214
I am stumped once again by another expectation value question. The question is as follows.
Alice, Bob and Charles play a game. In front of the players are four urns, each containing an equal number of balls of each of six different colours (red, orange, yellow, green, blue, and purple). In a single turn, a player draws a ball at random from each urn, aiming to draw four of the same colour. The four balls are then returned to the original urns and the turn ends.
In the final turn of a particular game, Alice draws 2 green balls, 1 blue and 1 red. Bob draws 3 red balls and 1 yellow. Charles finally draws 4 blue balls and wins. What is the expected number of rounds made by each player, including the final round, relative to each other?
There is so much information I have no idea where to begin. At first I was considering calculating the expected number of turns to obtain the particular combination they finally obtained and taking the ratio, but no information is given about previous turns. I am incredibly lost — please help!
Edit: this was multiple choice, and I believe the options were:
1) Charles played 5x as many rounds as Bob, who played 4x as many as Alice
2) Charles played 20x as many rounds as Bob, who played 4x as many as Alice
3) Charles played 5x as many rounds as Bob, who played 6x as many as Alice
4) Charles played 20x as many rounds as Bob, who played 6x as many as Alice
5) None of the above
I hope this clarifies things!
probability game-theory conditional-expectation expected-value
probability game-theory conditional-expectation expected-value
asked Nov 23 at 4:27
user107224
378214
asked Nov 23 at 4:27
user107224
378214
edited Nov 24 at 1:09
asked Nov 23 at 4:27
user107224
378214
asked Nov 23 at 4:27
user107224
378214
asked Nov 23 at 4:27
user107224
378214
378214
Hmm... It all made some sense before the words "relative to each other", after which I got lost too: how could it be that the players made different numbers of turns? I guess your best bet is just to ask whoever gave you this problem what exactly the conditions mean and what the question is.
– fedja
Nov 23 at 5:11
@fedja Hello, I’ve added options for clarity!
– user107224
Nov 23 at 8:07
Then my guess is that the intended answer is (4) (Compare the frequencies (=probabilities) of getting all 4 of one color, 3+1, and 2+1+1), but whoever formulated the problem the way it was stated was thoroughly confused about either the English language, or mathematics, or both, because the meaning conveyed has pretty much nothing to do with the meaning intended (Alice aims at exactly 2 of the same color to stop, Bob aims at exactly 3, Charles goes for all 4).
– fedja
Nov 23 at 11:31
add a comment |
Hmm... It all made some sense before the words "relative to each other", after which I got lost too: how could it be that the players made different numbers of turns? I guess your best bet is just to ask whoever gave you this problem what exactly the conditions mean and what the question is.
– fedja
Nov 23 at 5:11
@fedja Hello, I’ve added options for clarity!
– user107224
Nov 23 at 8:07
Then my guess is that the intended answer is (4) (Compare the frequencies (=probabilities) of getting all 4 of one color, 3+1, and 2+1+1), but whoever formulated the problem the way it was stated was thoroughly confused about either the English language, or mathematics, or both, because the meaning conveyed has pretty much nothing to do with the meaning intended (Alice aims at exactly 2 of the same color to stop, Bob aims at exactly 3, Charles goes for all 4).
– fedja
Nov 23 at 11:31
Hmm... It all made some sense before the words "relative to each other", after which I got lost too: how could it be that the players made different numbers of turns? I guess your best bet is just to ask whoever gave you this problem what exactly the conditions mean and what the question is.
– fedja
Nov 23 at 5:11
Hmm... It all made some sense before the words "relative to each other", after which I got lost too: how could it be that the players made different numbers of turns? I guess your best bet is just to ask whoever gave you this problem what exactly the conditions mean and what the question is.
– fedja
Nov 23 at 5:11
@fedja Hello, I’ve added options for clarity!
– user107224
Nov 23 at 8:07
@fedja Hello, I’ve added options for clarity!
– user107224
Nov 23 at 8:07
Then my guess is that the intended answer is (4) (Compare the frequencies (=probabilities) of getting all 4 of one color, 3+1, and 2+1+1), but whoever formulated the problem the way it was stated was thoroughly confused about either the English language, or mathematics, or both, because the meaning conveyed has pretty much nothing to do with the meaning intended (Alice aims at exactly 2 of the same color to stop, Bob aims at exactly 3, Charles goes for all 4).
– fedja
Nov 23 at 11:31
Then my guess is that the intended answer is (4) (Compare the frequencies (=probabilities) of getting all 4 of one color, 3+1, and 2+1+1), but whoever formulated the problem the way it was stated was thoroughly confused about either the English language, or mathematics, or both, because the meaning conveyed has pretty much nothing to do with the meaning intended (Alice aims at exactly 2 of the same color to stop, Bob aims at exactly 3, Charles goes for all 4).
– fedja
Nov 23 at 11:31
add a comment |
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Hmm... It all made some sense before the words "relative to each other", after which I got lost too: how could it be that the players made different numbers of turns? I guess your best bet is just to ask whoever gave you this problem what exactly the conditions mean and what the question is.
– fedja
Nov 23 at 5:11
@fedja Hello, I’ve added options for clarity!
– user107224
Nov 23 at 8:07
Then my guess is that the intended answer is (4) (Compare the frequencies (=probabilities) of getting all 4 of one color, 3+1, and 2+1+1), but whoever formulated the problem the way it was stated was thoroughly confused about either the English language, or mathematics, or both, because the meaning conveyed has pretty much nothing to do with the meaning intended (Alice aims at exactly 2 of the same color to stop, Bob aims at exactly 3, Charles goes for all 4).
– fedja
Nov 23 at 11:31