The sports minister Svilen Neykov ordered a special review after 4, 15, 23, 24, 35, and 42 were drawn on Sept 6 and again on Sept 10 in consecutive lottery rounds.
The probability of this happening is 4.2 million to one, according to the Bulgarian mathematician Mihail Konstantinov, although he added that such coincidences can happen.
Given that it has happened the probability of this happening is of course 1.
Err, no. If the probability was 1, it would happen every time.
Suppose you tossed a coin and it came up heads. Does that mean that the probability of a head in any coin toss is 1?
Tim adds: Err, yes. The probability of something which has happened is one. That does not mean that the probability of it happening in the future is one, of course (although given the number of lotteries there are around the world and the amount of time they’re likely to go on the probability does approach one).
Given that it happened *without cheating* the probability is 1.
But as we can’t be sure there wasn’t cheating the probability isn’t 1.
That bloody Derren Brown!
Ahh, yes. An event that has happened vs a possible event. Quite right. 6 penalty points on my pendant’s licence, plus 30 hours community grammar and parsing.
The probablilty that it happenED is 1. The probablity of it happenING is 1 in 4.2 million. The article used the future (conditional?, my grammar is not so good) tense, so it seems correct to me.
Then again, the probability of ANY stated result is exactly the same as the probability of any other stated result, whatever the previous result may have been, because each result is a single event.
There’s an epistemological difference between the truth values of past and future events and their probability values. Future truth values coincide with probability values; past truth values collapse to 0 or 1. Thus, there is a distinction to be drawn between the statements (in 1939) “if Germany invades England, it will win the war”, (in 1986) “if Germany had invaded England it would have won the war”, and the corresponding truth value “Germany invades England; wins war.” But in 1986 the truth value of this is zero, whereas the probability values are still epistemologically meaningful (if undecidable).
In this case, absent fraud, surprise is only meaningful a priori. This is quite likely nothing more than a latter-day version of the Gambler’s Fallacy.