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Probability of event occuring? is there a formula?


ok, so we have an event, lets say a telephone call that goes through to a team of upto 10 sales people each with their own unique probability of getting the call assigned to them. so if all 10 are at their desks, the call has a 100% chance of being answered. but once person leaves their desk, the probability will fall by that amount. my question is, is their a formula that can show this all the way down to if only one person is at their desk?

many thanks

and what is the formula?

well yaybob's answer was pretty much all theres to it, but you said that each has a unique probability, so u cant really represent each person with a single pronumeral, since they have unique ones, they would need a separate pronumeral for each, meaning a different amount is subtracted according to who leaves

so a more accurate but more incovenient way to put it would be

Probability of call being answered = 100 - the sum of the probabilities that the call would go to any who have left

Yes. I'm assuming that you mean only one person's phone rings, and that if he is at his desk, he answers it, but that if he is away, nobody answers it. If n is the number of people away from his desk, then (10 - n) remain, and the odds of the call going to one of those people is

p = (10 - n) / 10

the same as the odds of the call being answered. In percent, this is

p% = 100% x [(10 - n) / 10]

Thus, if all 10 are present, n = 0 and p = 100%, whereas if all 10 are away, n = 10 and p = 0% If you would prefer the formula set up so that n stands for the number of people present instead of the number absent, it would look lke this:

p = n / 10

or in percent,

p% = 100% (n / 10)

Actually, this is a very complex problem called a "multi-server queuing system" with an infinite calling population. The assumptions are: first-come, first-served queuing discipline with Poisson arrivals and exponential service times.
You want formulas? There are plenty, but are too complex to show here. The calculations do not require calculus but are tedious.
If you are really interested, find a book on Management Science or Operations Research, and go to the chapter on queuing analysis and find the explanation of "Multi-server waiting line".

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