When is proof not proof?

This is a story (with a moral) about an HQ type office, of a large corporation, in a big city. 

It had been noticed, by the staff, that one of the middle-aged male executives and a younger female supervisor, both sparkle in each other’s presence, although no obvious social contact takes place between them. 

A rumour starts.

She lives to the east and he to the west.  Sure enough, on Friday evenings, he has been seen to head east, after work. The rumour escalates. 

One of the young guns decides to follow him.  About 5 miles out of town, the exec stops to buy flowers.  The youngster drives past and ceases to follow, suspicions strengthened.  Next working day he reports back, and the rumour strengthens again. 

But no smoking gun yet.  So next Friday, the exec is followed again.  This time, the pursuit continues until, a few miles later, the exec turns into a care home car park, parks, and takes the flowers inside.  After an hour he has not emerged, so the sleuth goes home, concluding they have all been barking up the wrong tree.  And so, on Monday, he duly reports back and the rumour dies.

Meanwhile, though, after his care home visit, to his grandmother, the exec had headed off to have dinner and “afters” with the young lady supervisor.  Story to wife: “I’ll visit grandma, and, as it’ll be late, I’ll stay overnight in a hotel.”

The moral of that story is not to jump to conclusions till you have all the data. This was a favourite ruse of Agatha Christie, of course (which is why I like watching Poirot on tv).

Now try to think of as many theories, or predictions, as you can, that have been “proved correct” on the basis of a limited amount of evidence...........