# Help working out virus exposure probability(?) in an office

#### CjD

##### New Member
Hi,

I would like some help with working out virus exposure risk/probability/chance in a workplace. I know nothing about stats/probability and this may be really easy but I just don’t know. What would be really useful is a formula so I can feed in different numbers and get a figure that might help with decision making.

Question
What is the probability (or is it chance) of someone in an office having the virus?

Variables
Official virus rate in a community = 50 per 100,000 people
Community size = 200,000 people
Office size = 10 people (all from this community)

More Questions:
What happens to the figure if the community virus rate doubles?
What happens to the figure if the office size doubles or if it halves?
… this may just be dividing or multiplying by 2 but is it that simple?

If the community virus rate doubles, does halving the number of people in the office keep the exposure risk the same?

Any help greatly appreciated. The last maths I did was for an O Level in the 1980's (I got a C) and I can still hear my teacher’s voice saying “pay attention, you will need this one day…”

#### hlsmith

##### Less is more. Stay pure. Stay poor.
For the way you presented this, given the community rate is accurate and representative, yes it is as simple as generalizing that rate to office. If it doubles you would generalize that new rate. Just think about people with a virus as blue marbles in a bag full of white marbles. The probability a random person has the virus is equal to randomly pulling a blue marble out. As for risk and exposure, those are different from what you are writing about and deal with transmission variables, which aren't available given you data.

Now if we are actually talking about real-life scenarios (e.g., COVID), it would also be beneficial to know the susceptibles. Meaning currently there is only one documented case of re-exposure. So if anyone in the population has had the virus and cleared it or are not longer contagious, they are no longer at risk of getting it again. For a basic introduction, look at SIR (susceptible, infected, recovered) models.

#### CjD

##### New Member
I should not have mentioned risk or exposure, I am not considering any other factors such as available PPE, proximity, exposure duration, etc. I just want it very simple at the moment, just the probability someone has a the virus in the office using some official stats. I realise now that I will need to look at SIR as the Recovered variable will be increasingly important. It is actually the number of asymptomatic or very mild cases I am concerned with but this is a starting point.

So for now, is this correct:
100 infected in 200,000 = 1 person in 2000
If the office has 10 people it is 10/2000 or 1 in 200
If the office has 20 people it becomes 20/2000 or 1 in 100

Is it that simple?

Is it correct to say this: if we have 10 people in each office and we have 200 offices in this community we should expect (it is probable) that 1 person will have the virus?

This scenario is quite close to our actual situation but we run training courses for small groups of about 10 - 20 adults. All random strangers and only on the courses for a few hours to a few days.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I think you are off. So if the infected rate was 0.05%, you just take whatever number you are interested in times it by 0.0005. So in your office expect 10 * 0.0005 people to be infected. Big picture, for every 2000 employees expect one to be infected.

Is it correct to say this: if we have 10 people in each office and we have 200 offices in this community we should expect (it is probable) that 1 person will have the virus? Yesl