In his little book, Insight, Lonergan has this wonderful remark about the relative probabilities of an unconnected aggregate of events, and a connected set of events that he calls 'scheme of recurrence.' The probability of the former, he points out, is the product of the individual probabilities, while the probability of the latter is the sum of the individual probabilities.
Since probabilities can be written in terms of fractions, it is easy to see that the product of a set of fractions is far smaller than the sum of the same set of fractions.
Which means that the probability of an event occurring jumps when it forms part of a scheme of recurrence.
Some months ago I had a wait-listed ticket from Thivim to Dadar which eventually became RAC. That meant I could board the train, but it also meant that I had only a seat: I had to share a berth with someone else. Now if you have ever shared a berth on an Indian train, you will know what that means. But my point here is different: the point is that, despite the fact that I had a rather good wait-list number (I think it was in single digits), all I got was an RAC seat, and not a proper berth. I discovered the reason for that in the train: there was a huge college tour group on the train that day. The TC pointed out that such groups do not easily change their reservations. If there was no such group, he said, I would have stood a better chance of getting a berth for myself.
Now here is an interesting situation: a group, vs a set of unconnected people. The probability of my getting a berth would have been higher in the latter case.
How would that compare with Lonergan's remarks? I am still trying to work that one out... Any help?