[boubette]

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!

[ebaines]

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?

[InfoJunkie4Life]

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.

[galactus]

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.

[ebaines]

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