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Probability that two uniform boxes are in the same part of a uniform composition
Why the two probability results are the same?$N$ balls and $M$ boxes, probability of last $ i$ boxes are empty, non uniform probabilityAsymptotically, how many random students do I have to mark before I've marked two consecutive studentsProbability that two sets are disjoint? the same?Probability that two multinomial samples are the same?Probability with two boxes and ballsmodels of coins and uniform distributionProbability that the withdrawn balls are the same colorWhat is the probability of winning Casino War?Probability that in two sequences of trials there are the same number of success
$begingroup$
We consider a uniform composition of $k$ in $alpha$ parts (seen as a sequence of $k$ boxes and $alpha -1$ bars) and we ask what is the probability that two uniformly distinguished boxes are contained in the same part.
Summing over all the possibilities (with terrible computations) I found the following nice formula for this probability;
$$frac2alpha+1cdotfrack-ak-1$$
Does anyone have an easy explanation of this surprisingly nice formula?
probability combinatorics probability-theory binomial-coefficients
asked Mar 22 at 8:49
bojicabojica
282115
$endgroup$
add a comment |
$begingroup$
We consider a uniform composition of $k$ in $alpha$ parts (seen as a sequence of $k$ boxes and $alpha -1$ bars) and we ask what is the probability that two uniformly distinguished boxes are contained in the same part.
Summing over all the possibilities (with terrible computations) I found the following nice formula for this probability;
$$frac2alpha+1cdotfrack-ak-1$$
Does anyone have an easy explanation of this surprisingly nice formula?
probability combinatorics probability-theory binomial-coefficients
asked Mar 22 at 8:49
bojicabojica
282115
$endgroup$
add a comment |
$begingroup$
We consider a uniform composition of $k$ in $alpha$ parts (seen as a sequence of $k$ boxes and $alpha -1$ bars) and we ask what is the probability that two uniformly distinguished boxes are contained in the same part.
Summing over all the possibilities (with terrible computations) I found the following nice formula for this probability;
$$frac2alpha+1cdotfrack-ak-1$$
Does anyone have an easy explanation of this surprisingly nice formula?
probability combinatorics probability-theory binomial-coefficients
asked Mar 22 at 8:49
bojicabojica
282115
$endgroup$
We consider a uniform composition of $k$ in $alpha$ parts (seen as a sequence of $k$ boxes and $alpha -1$ bars) and we ask what is the probability that two uniformly distinguished boxes are contained in the same part.
Summing over all the possibilities (with terrible computations) I found the following nice formula for this probability;
$$frac2alpha+1cdotfrack-ak-1$$
Does anyone have an easy explanation of this surprisingly nice formula?
probability combinatorics probability-theory binomial-coefficients
probability combinatorics probability-theory binomial-coefficients
asked Mar 22 at 8:49
bojicabojica
282115
asked Mar 22 at 8:49
bojicabojica
282115
asked Mar 22 at 8:49
bojicabojica
282115
asked Mar 22 at 8:49
bojicabojica
282115
asked Mar 22 at 8:49
bojicabojica
282115
282115
add a comment |
add a comment |
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