The average number of cards retained by mistake during a month by two ATMs of a bank is 1 in 10,000 for the first and 1 in 5,000 for the second. Given that during a specific year 15 cards were retained in total by both ATMs, what is the probability that 8 of them were retained by the first machine? Please help me with the question!

Boubette - I think you have left out some important information, which makes it impossible to answer this queston. Specifically - can you tell us how many cards were used in each machine?

I am thinking that statistically speaking 2/3 of the retained cards should be held by the second considering that it retains twice as many. I'm not too good in statistics, but it would seem to me that the 8/15 would somehow be influenced by the 2/3 ratio probability.

Just thinking aloud (or awrite?) here. Don't quote me, and I'm not saying I'm right either... just throwing out some ideas and assumptions... getting the train rolling.

We may be able to use a hypergeometric probability here.
The problem spans over a year, but the probabilities given are for one month.
If 15 are kept by machine 1, then the other 7 are kept by machine 2.
Doing this, I get .115 as the probability that 8 out of 15 are kept by machine 1.

Seem reasonable?

It most likely doesn't matter anyway because I doubt if the poster repsonds back.

Galactus - you are assuming that an equal number of cards were used in each ATM, right?