If I were to pick numbers for a lottery perhaps, would a sequence like that be a bad idea?
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In a lottery, that particular sequence is exactly as likely as any other specific 7-digit sequence.
For instance, the sequence 3-2-0-1-9-5-8 is exactly as likely as the sequence 1-2-3-4-5-6-7. If the lottery number is 7 digits between 0-9, you have 10 options for each number in the sequence, and therefore the total number of possible sequences is 10^(7), or 10 million, and so each of the two sequences above has a 1 in 10 million chance of winning.
If you’re asking: how likely is it that the winning lottery number will be a “meaningful” sequence like 1-2-3-4-5-6-7, as opposed to some meaningless sequence, then the answer is slightly different. Out of all 10 million possible numbers, the vast majority are meaningless to most people. Let’s say there are only 1000 “meaningful” 7-digit sequences out of all 10 million possibilities. Then that means the odds of the winning lottery number being a “meaningful” number are 1 in 10,000.
Wait a minute, doesn’t that contradict what I said earlier? Doesn’t this imply you shouldn’t pick a meaningful number? Well, no. Because while it is more likely that the winning lottery number will be one of the 9,999,000 “meaningless” numbers, there are also 9,999,000 of them. So even though the odds of the number being in the meaningless set are 9999 in 10,000, you have to multiply that by the odds of your number being the winning one within that set, which are 1 in 9,999,000. And 9999/1000 times 1/9,999,000 equals, you guessed it: 1 in 10 million. We can do the same for the meaningful set: the probability that the winning number will be from this set is 1 in 10,000. Given that the winning number is in that set, and that you picked a number from that set, the chance that yours is the winning one is 1 in 1000. 1/10,000 times 1/1000 equals, once again 1 in 10 million.
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