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In the Bain case we are required to weigh up multiple independent items of evidence. In order to achieve a balance of probabilities we can use math to do some of the heavy work for us. This allows us to focus on the essential items of evidence themselves and make reasoned decisions about them, while allowing the overall balance to be calculated in a relatively objective manner.
To each item of evidence we consider the probability that that item implicates David or Robin in the overall crime. Instead of using words like 'likely', 'probable', 'speculative' etc. we use a number, a probability, which in this case is between 0 and 100. 0% probability means that we think that there is definitely no connection and 100% probability means that the connection is definite. For instance, if we think that there is sufficient cause to say that the bloody footprints probably belonged to Robin, then since it is agreed that those footprints belonged to the killer, we could assign 75% probability to Robin in that item. If, however we think that it could be equally either Robin or David, then we would put 50% for each. Some items of evidence might be incidental, in that they actually have nothing to do with the crime. While it is clear that the bloody footprints were definitely involved, it is possible that the glasses were not, and that was an arguement put by the Defence. You would expect, therefore to have a value for incidental probability for that item, which represents the probability that the item had no connection with the crime.
We can also assign different weights to each item reflecting how compelling that item is. For instance items of evidence involving forensic science tend to be more compelling than hearsay testimony. Having the weight allows us to include more items of evidence and to give each item the importance we think it deserves. Items with a higher weight have a greater effect on the overall probability. If you think that an item plays no part in the crime, then assign a 0 weight to it and it will not be included.