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## Main Question or Discussion Point

Hi all

I recently ran into this problem:

I have two bins. Each bin contains N numbered balls, from 1 to N.

For both the bins, the probability of the ball numbered k to be

selected equals to P(ball-k-selected)=k/SUM(1:N) (in other versions

this can be any given probability distribution)

Having selected 1 ball from the first bin, and 1 ball from

the second bin, i want to find the probability of the ball

having the same number.

If i am correct, the probability for this is SUM(k=1:N) (P(ball-k-selected)^2).

Having selected m balls from the first bin, and m balls from

the second bin, i need the probability of holding at least

one pair of balls with the same number at the end of the

experiment.

Assumption: The selection is without replacement. However, for

simplicity we can assume that the probability of a ball to be selected

remains stable during the experiment, and is given by

P(ball-k-selected)=k/SUM(1:N)

If something is not clear, please let me know.

Thanks in advance for any contributions!

I recently ran into this problem:

I have two bins. Each bin contains N numbered balls, from 1 to N.

For both the bins, the probability of the ball numbered k to be

selected equals to P(ball-k-selected)=k/SUM(1:N) (in other versions

this can be any given probability distribution)

**Simple case:**Having selected 1 ball from the first bin, and 1 ball from

the second bin, i want to find the probability of the ball

having the same number.

If i am correct, the probability for this is SUM(k=1:N) (P(ball-k-selected)^2).

**Complex case:**Having selected m balls from the first bin, and m balls from

the second bin, i need the probability of holding at least

one pair of balls with the same number at the end of the

experiment.

Assumption: The selection is without replacement. However, for

simplicity we can assume that the probability of a ball to be selected

remains stable during the experiment, and is given by

P(ball-k-selected)=k/SUM(1:N)

If something is not clear, please let me know.

Thanks in advance for any contributions!