On employees theft rate < Wahrscheinlichkeit < Stochastik < Oberstufe < Schule < Mathe < Vorhilfe
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(Frage) beantwortet  | | Datum: | 22:27 Do 29.10.2009 | | Autor: | jonsox |
Hi all
Recently I had an argument with a few colleagues @ work because of laptop that has been stolen.
As background information I am working as a clerk in a bank. The guys went on stating that the people responsible for keeping
our workplaces neat and tidy were the ones who stole it because it is more probable that they need the money. Althou this kind of
seems to be logical I wanted to explain to them that this was a merely assumption with no meaning and on my way home I thought about the following;
Let us say there are 1060 people working in a bank. Of those 1060, 60 people are responsible for cleaning and 1000 are working as bankers.
My assumptions
Group A = consisting of 60 members. Within this group the probability of somebody stealing a laptop is 5%
Group B = consisting of 1000 members. Within this group the probability of somebody stealing a laptop is 1%
Does it follow that;
The probability of a laptop beeing stoled (independent wheter is somebody of Group A or Group B) is 6% ?
What can I deduce from the fact that it is more probable that Group A steals more than Group B ?
I mean, if the expected probability of somebody from;
Group A is 60 times 5% = 3 Persons
and
Group B is 1000 times 1% = 10 Persons stealing a laptop
If Group A would consist of 1000 Persons this would mean that 60 persons would steal a laptop (lets assume linearity here), but since
this is not the case because the bank has merely 1060 this is a meaningless result.
Could I say that;
- It is indeed more probable that a person who is cleaning up the facilities in which we work is more likely to steal a laptop becaue the probability is higher (6% >1%), but
since more people are working as bankers and 3 people out of group A are less then 10 people out of group B, it is more likely that when a laptop gets stolen it might have
been a banker the one who is to be the culprit ? (This is actually what I believe, but since my level of statistics is very low, I would really appreciate some help. I found it damn of my colleagues @ work to make me listnening to an indistilled way of making assumtions based on nothing but their subjective non empitical expirience merely disgusting).
I hope somebody does help me on this one so I can print this out and hang it on the entry of my office for everyone to read it.
Thank you all in advance
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(Antwort) fertig  | | Datum: | 11:39 Fr 30.10.2009 | | Autor: | leduart |
Hello
Do you want an explanation? Please state your question clearly.
The probability you give ist unclear.
do you mean it is probable, that in a given fixed time, say one year, the probability, that 5% of your group A steals a laptop is very high, approx. 100%, and of Group B 1%
Than you will have an average of 13 stolen laptops per year,
3/13 stolen by members of group A, 10/13 by members of group B.
So the probability of one specific laptop beeing stolen by a banker would be 3.3 times as high, as the prob. for a cleaning person.
Gruss leduart
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