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for example, I have 7 customer bookings in a day, each with an independent probability of show up. So what is the probability of only 1 customer show up? only 2 customers show up? only 3 customers show up? etc. How to compute this type of problem, is there any generalized equation or formula ?

Customer Probability of show up Probability of not show up
A 0.3 0.7
B 0.4 0.6
C 0.5 0.5
D 0.6 0.4
E 0.7 0.3
F 0.8 0.2
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1 Answers1

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I don't know of any formula, but you can calculate the probabilities of n customers turning up like this:

Let p[i] be the probability of customer i turning up. Let Q( N, n) be the probability that, if we consider just customers 0,..N-1, then n of them turn up.

We have

Q( 1, 0) = 1.0-p[0]
Q( 1, 1) = p[0]

And

Q( N+1, 0) = (1.0-p[N])*Q(N, 0)
for i=1..N
    Q( N+1, i) = (1.0-p[N])*Q(N, i) + p[N]*Q(N, i-1)
Q( N+1, N+1) = p[N]*Q(N, N)

For example, there are two mutually exclusive ways that i of customers 0..N can turn up: either customer N doesn't turn up and i of 0..N-1 do, or N does turn up and i-1 of 0..N-1 do

dmuir
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