Math problem

chielsen

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So I know there are alot of math geeks out here so i'll give it a shot.
I was wondering the following. What is the chance there is no transaction on a working day in a month. All transaction on saturdays and sundays gets passed to the next monday.

T = number of transactions (40)
D = days in a month (30.44)
W = working days in a month (21.67)

At first i did not take into account working days, so i had:
poissonPdf(40/30.44,0)

Then i thought well maybe with working days it's:
poissonPdf(40/21.67,0)

But now i'm beginning to wonder. The monday gets all the transaction of saturday and sunday too, but the other days don't. So they are more likely to have no transaction than if there were only working days.

Is this right or should i do it differently?
 
Maybe this:

poissonPdf(3*$payments/30.44,0) + 4 * poissonPdf($payments/30.44,0)) /5

?
 
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