Statistics 101

This, I think, is wrong. Perhaps I am simply reading these isolated sentences out of context and am missing your point. In that event, I apologize.Once the lottery numbers have been drawn, the probability of winning with a ticket that you purchased before the drawing are either 0 or 1, depending on whether you matched. The fact that you do not know what the outcome is does not change the probability. It is something that has already happened. The probability for any past event is always either 0 or 1.Consider a game of draw poker where you have the 10, Jack, Queen and King of spades. What is the probability of drawing the Ace to make a royal flush? Assuming that the deck has already been shuffled and no further mixing of the cards will take place, the probability is either 1 or zero, depending on whether or not the Ace is on the top of the deck. We treat the situation as if the probability is 1 in 47 because that's all the information that we have. But our lack of information does not make the actual sequence of cards set at the time of shuffling indeterminate, or a matter of chance. The order of the cards is what it is.Edited by subbie, : No reason given.

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Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin FranklinWe see monsters where science shows us windmills. -- Phat

We are talking about two different things, I think.I am talking about the probability of an event happening that has already happened. You seem to be talking about the probability before the event happens.I don't know what you mean when you say "probabilistic nonsense." To me, it is nonsense to talk about the probability of an event that has already happened. It either did or it didn't. Once again, lack of knowledge about the outcome of an event that has already happened doesn't mean that there is a probability of the event going one way or another.

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Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin FranklinWe see monsters where science shows us windmills. -- Phat

Perhaps we are just arguing semantics.dictionary.com says this:

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4. Statistics.
a. the relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences.
b. the relative frequency with which an event occurs or is likely to occur.

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Wikipedia says this:

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Probability is the extent to which something is likely to happen or be the case.

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Under the first usage from dictionary.com, I stand by what I said. It's meaningless to talk about the probability of something that has already happened. The relative possibility that I was born on an even-numbered day is 1, because there are no other possibilities. The relative possibility that my first grandchild will be born on an even-numbered day (assuming I will have one) is 1/2, because that event has not yet happened. Once any event has happened, the relative possibility of that event is 1 because there are no other possible occurrences.It seems to me that you are using the term more in accordance with the second usage from dictionary.com and the Wiki definition, although Wiki seems ambiguous and could be consistent with my usage. In that sense, you are correct that the relative frequencies of the different possibilities of random events do not change simply because one outcome has been determined.

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Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin FranklinWe see monsters where science shows us windmills. -- Phat

I disagree.The probability, under the first definition from dictionary.com above, of a past event happening is either 0 or 1. It either happened or it didn't. It makes no sense to say that the odds are 146 million to 1 given the information you have. Your information doesn't change the outcome of a past event. Likewise, the mere fact that we don't know what the next card is doesn't affect the card.Certainly, gamblers use probability calculations all the time in determining whether to bet on a given outcome. And, given that the outcome is unknown, it's reasonable for them to do so. However, in the example of a deck of cards, no calculation or discussion of probability will change the identity of the next card to come.

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Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin FranklinWe see monsters where science shows us windmills. -- Phat

Hmmmmm, where to start....It's not possible to fully determine the probability of either woman winning because you didn't specify the odds of winning. You specified the number of tickets bought, but that doesn't have to have any relation to the probability of winning. Moreover, it's not possible to determine the probable winning payouts necessarily based on the number of tickets sold.I assume that you were trying to describe a situation where Mrs. Smith had a higher probability of winning than Mrs. Jones. In that situation, it would be accurate to say that Mrs. Jones was luckier than Mrs. Smith.As far as which meaning of the word has more utility, I suppose that all depends on what one is trying to say.

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Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin FranklinWe see monsters where science shows us windmills. -- Phat