Hi all(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Probabilities: Estimating the probability of overlapping

Loading...

Similar Threads for Probabilities Estimating probability |
---|

I Non-countable uniform spaces probability |

I Probability of equally likely events |

A How to calculate the probability of error in an AWGN channel? |

A Sum of independent random variables and Normalization |

I Checking for Biased/Consistency |

**Physics Forums | Science Articles, Homework Help, Discussion**