Subbie,
Suppose Mrs. Smith is one of a million people who have bought a lottery ticket. In the lottery, only one ticket is drawn, and a million dollars is paid out to the winner. The ticket drawn happens to be Mrs. Smith's.
Mrs. Jones has also bought a ticket in another lottery, in which ten million people take part. In this lottery too, one ticket is drawn and a million dollars paid out to the winner. It so happens that Mrs. Jones' ticket wins her a million dollars too.
In retrospect, how should we assess Mrs. Smith's luck in relation to Mrs. Jones'?
We can say: "Well, Mrs. Smith's winning a million dollars has already happened, so the probability of that occurence is 1. Likewise, the probability of Mrs. Jones' winning a million dollars is also 1, because it has already happened. Therefore, both women were equally lucky. Besides, any statement about Mrs. Smith's and Mrs. Jones' luck in their respective lotteries, after the fact, is meaningless."
Or we can say: "There were a million people buying a lottery ticket in Mrs. Smith's case, and ten million in Mrs. Jones' case, so Mrs. Jones' chance of winning a million dollars was ten times less than that of Mrs. Smith's. Therefore, Mrs Jones was ten times more lucky than Mrs. Smith."
Which meaning of the word 'probability' has more utility, you think?
Edited by Parasomnium, : No reason given.
"Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science." - Charles Darwin.