The Chances Of Meeting An Infected Person...

[BilSuth]

depend on the percentage out there, and how many you meet. The fewer the better, obviously. I'm not talking about the chances of getting infected because distancing, maybe masks and other protections affect that calculation.
Not many people actually believe that if you throw dice six times, any given number is "certain" to come up. In fact, the chances of it NOT coming up are 5/6 to the power 6 or .33489. So the chances of success are .66511, roughly 2 out of 3.
It's a long time since I did calculus, stats and anything else related but I know that the formula for this would be (n-1)/n to the power n. This formula reveals that the higher value of n, the closer we get to .367879 or thereabouts (I've tried it to some high values e.g. 1million). That of course is the NON-event decimal; we have to deduct it from 1 to get our "success" answer, i.e. .632121 ... approximately.
Maybe one of you scholars out there can remind me about iterations, attractive fixed points, or whatever kind of sequence defines this formula.
Meantime, keep the odds down and stay safe, folks. One infected person can be one too many.

[Peter Pedant]

what ya describing is stochastic modelling of covirus and I havent seen one
the usual one used is the S - I - R model which I have referenced other place but go to You tube and search "epidemiology zhukov "

Neil Ferge is flavour of the month and uses SIR models
and all the hard work is going into whether the parameters are accurate or not

oh and the answer is the ratio of number in the infected pool over the number in the susceptible pool
this is a time dependent variable

[BilSuth]

Thanks, Peter. I'm not trying to evaluate the chances of actually getting infected, which is your sensible and relevant area of discussion, but just "... chances of meeting someone... " simply to trot out my old probability formula for discussion and just put it into the Covid context. If the experts suspect that the real local infection rate were to be (say) 1% of the population, then I would not like to encounter any more than about five, even keeping distance, otherwise it gets very scary.

[jim360]

I think you could interpret the SIR model as a probability that *you* catch the disease assuming you're a normal random citizen. Going much beyond that would be tricky.

If it helps the original problem, it's worth noting that 1/e = 0.3678794...

[BilSuth]

Jim, where does "e" come from, in your 1/e ? What value or context is this? Interesting if another, established formula gets to the same decimal area.

[jim360]

"e" here is 2.71828... , and it arises because in fact one definition of it is simply that e = \lim_{n \to \infty} (1+(1/n))^n . To get to 1/e it's enough to replace the + sign there with a minus sign.

[BilSuth]

I get that, Jim, but how does it relate to {(n-1)/n}^n ?

[fiction-factory]

(n-1)/n = 1- (1/n) if that helps.
Sorry, realise you may know that.

[10ClarionSt]

This is like a judge and barrister discussing a case in latin.

[Old_Geezer]

I'm going to wait until then come up with a percentage for their conclusion.

[jim360]

Maybe it's better to start over, if you still have questions feel free to ask and I'll try to answer more clearly this time.

[youngmafbog]

Depends on if you are an avid player of real Russian Roulette. Because that is what is is since no one actually knows where it is or real percentages since not all people are reporting it and carriers certainly dont.

[Peter Pedant]

// This is like a judge and barrister discussing a case in latin//
or the Dook of edinburgh might say:
ots all greek to me

good morning gentlemen - a sensible discussion not marred by some bag lady telling Jim " Mr Russell - your ideas just arent logical!"
yup Lady Cunard ( basis for Margot Metroland in Waughs VileBodies) to Bertrand Russell

the thing about stochasm - er stochastic studies is that you start ort widda delta-t for the instant or time and the chance of meeting one infected ( rho or something)
then the chance of meeting one if dt is small enough is p-dt
and there is no chance in that instant of meeting two

and off you go! - poisson process comes up of course and exponents. used a lot in queuing - yup queuing - but I havent seen it in infections

as wivva lot of models - the maff is the same ( Hi FF! and Hi Jim Happy Palm Sunday ) but the spplications and assumptions from real life are different - and may give wildly different answers

( like the school of Oxford - "epidemic what epidemic?" - whats happened to them ? quiet they are - muffled if not dead)

I havent met a doctor coming off a duty shift
who says epidemic what epidemic

[andy-hughes]

The problem is, who wants to play 'chance' with a potentially fatal dose of a virus?

I am sure there is a formula in favour of the chances of you not getting knocked down if you crossed the 6 blindfold - but that doesn't mean I'd put it to the test!

[jim360]

That's true, of course. Still, there's some morbid comfort to be derived from the amount of data analysis and mathematical modelling experience you can rack up while a pandemic is progressing.

[Peter Pedant]

ex = how does it relate to {(n-1)/n}^n ?

because you expand ex according to er the usual expansion
one plus ecks plus eclks sqaured etc

and expand the other one according to the binomial theorem
and let n -> 0 ( get farry leedol in AB speak)
and get the same expansion and so low and hehold
the identity is established.

and thx to Fatty Barrett who is around 95 now and taught me that when he was fifty

[jim360]

Even I have trouble understanding your posts sometimes :/

[Peter Pedant]

oh I was taught in a mixed ability adult maff class and at one point the maff toot said to me " you dont think symbolically do you?"

[Peter Pedant]

oh come on come on - e and the binomial theorem Jum you did this at A level - - - Jim " did I ? it was all so long ago...."
start concentrating at sec = 1

[Mozz71]

I started to read Jim and Bil's exchanges, but had to stop when the nose bleeds started. You're either far more intelligent than I, or waffling uncontrollably.

I rather suspect it's the former option.

[Peter Pedant]

someone asked - someone asked for chrissakes
// I get that, Jim, but how does it relate to {(n-1)/n}^n ?/
and the answer ( if we look at it that is.....) is in the viddie