¶ … love biking but have, unfortunately, gone through several different bikes in my life. Some of them have been stolen, others have been lost, others have just broken down and the cost of repairing them has been too great. Usually, I go for the cheapest bikes that I can busy, straight out from some supermarket package, but this time I am intending to spend my hard-earned money in a beatific model, something like Trek or Raleigh. I have been perusing consumerist's magazines for months ahead of time and am finally ready to make my purchase. I am intending to use probability concepts to help me. This is what I will do:

I only have a limited amount of places to choose from.

The first place is a second-hand store. There is 'subjective' probability' and there is 'objective' probability; likely, my judgment will be made from a combination of both: the objective probability based on what I see and soliciting advice from the storeowner, and the subjective probability based on my own experience of what I want and what failed me in the past.

Probability ranges from 0 to 1. In other words, 0 represents absolute certainty that I will not obtain my desired bike from this place, whilst 1 represents absolute certainty that the bike will possess all required elements.

The characteristics of...

I also of course want a cheap bike. If I get a bike that has all of these and more the sum of the probabilities of my getting this bike is 1. The sum of my not getting this bike, on the other hand, is 0.
Some of my conditions may constitute non-mutually exclusive events, i.e. I may have to retract on one or more of my conditions. For instance, the bike of my dreams may be expensive in which case I may have to retract on price or quality. In order to determine the probability that either event X (e.g. low price) occurs or event Y (e.g. quality) occurs, I add individual probabilities of event X and event Y, and subtract the probability that the two occur simultaneously from the total. Like this:

(P (x or y) = P (x) +P (y) -- P (x+y).

Probability tree diagrams

I need the bike as soon as possible for, frankly, I cannot live without a bike, and my last one has recently been stolen. I want a good one therefore want o research various places, but also want to limit myself in my search so as not to drive myself crazy. These are the places I can buy a bike from: used places, new, online, Craig's List, e-Bay, consult friends, news ads, or…