# Probabilities

#### geeman

##### New Member
Hi,
Whilst this isn't home work but work related, been a long time since I have brushed on my statistics but spent some time here trying to look at some posts and probably has confused me more. I am required to calculate probabilities of failing KPI's/event occurring 'x' amount of times per year. A couple of examples.

Task 1: "I will fail to produce my monthly report"
My assumption: "I think I will fail this 2 times per year".

Task 2: "I will forget to return client calls"
My assumption: "I think I will fail this 4 times per year".

Task 3: "I break the wifi router". (lets assume it will be offline for 3 hours - do I even need this level of data)
My assumption: "Probably fail this 2 times per year".

Where I am getting confused is around the 'time periods' for example in task 3.
I will break the wifi router 2x per year, is the probability calculated as:
a) 2/365? (2 days out of 365 days)
b) 6/8760? (6hrs out of 8760 hours per year)
c) 2/12 (2 separate months per year)

Hope this makes sense. For example and a practical purpose: I will have to have a managers meeting every 3 months to determine if I have "broken any KPI's" so should everything be evaluated in quarters/3 months? or perhaps even granular in months?

#### katxt

##### Active Member
I am required to calculate probabilities of failing KPI's/event occurring 'x' amount of times per year.
Do they want actual probability statements like "There is a 20% chance that I will fail Task 2 four or more times in the next year."?

#### fed2

##### Active Member
i think this company officially has too much middle management...

#### geeman

##### New Member
Lol agreed, there are statements like that. So I have to make certain assumptions, but am confused calculating the probabilities

#### katxt

##### Active Member
I am required to calculate probabilities of failing KPI's/event occurring 'x' amount of times per year.
Looking at your examples, I imagine that you should work in events per year.
My assumption: "I think I will fail this 4 times per year".
Given an estimate like this and some reasonable assumptions, you can make statements like "there is about a 60% chance that I will make 4 or less failures this coming year" Or, "I'm 90% sure that there will 6 at most this coming year".
Is this the sort of thing you want, with some sort of justification?

#### geeman

##### New Member
Yes @katxt there are assumptions at play which I will base the stats on.
For the purposes of this discussion i'll use the following example:
We have a wifi router, using data and experience we can say that we expect it to have 1 fault every year, and every time the wifi router gets a fault I get a $5 fine. So in this example is the probability calculated as 1/365? = 0.3% To make it practical in excel, I will have Jan to Dec across the top (12 columns for 5 years so 60 columns all up), and in each column i essential want it to randomly simulate in which month i will break the wifi router, essentially over 5 years or 60months, in each month there is a 0.3% chance I will break the Wifi router so I will get docked$5 when that occurs.

The second part is fine, as its an external software that will run monte carlo simulation, running 1,000s of simulations to randomly plot in which month I will break the router. Where I was getting confused is the calculation of probabilities, really like step 2 of the process (after making assumptions)

#### katxt

##### Active Member
I'm a bit confused now.
Choose the time period. It sounds like you are using a month. Then convert everything to that (months, say). 1 fault per year is 1/12 fault per month on average. Your simulator will allocate a fault or not each month by virtually tossing a 12 sided die.
In a simple situation like this, you could work out what will happen without a simulator if you want to.