I would very much appreciate your input on the following probability model description I’ve been working on. It’s been some 35 years since I used my Statistics degree in anger, so apologies if my technique is a little rusty.

Let P be the probability that some muppet will ring the doorbell at the most inconvenient time.

The value of P can be increased by:

a) The optimum point of time spent in the shower at which point the ringing of a doorbell would cause maximum inconvenience – call it S. The value of S is assumed to follow its own Normal distribution, whereby the optimum point of inconvenience would be at the peak of the bell-shaped curve. At this point, one would be fully soaped up and about to commence the rinsing process (R). The value of S remains high until the use of a towel has begun and R increases to 100%. We must not forget to incorporate the value of D which is the level of difficulty involved in putting dry clothes onto a wet body when P reaches 1. The value of D will decrease in direct proportion to the time spent toweling your bits off.

b) The proximity of your bottom to the lavatory seat (B) and the function undertaken (F1 and/or F2), with the latter being a more complex operation. The value of P increases as B reaches a value of 1. At this point, P is then determined by the time (T) B remains at 1 and the progress of F1/F2. P reduces significantly as F1 approaches 100% and the plotted graph is therefore assumed to be left-skewed. However, because of the complexity of F2, the value of P remains high right up until F (the flushing operation) has been reached and is therefore assumed to be right-skewed when plotted.

Question: Can a single formula be created to determine P for both situations?