[Edit 14.8.25: This has caused some confusion. To clarify, I’m looking for the chance of ANY 10-digit sequence being selected first, using all the digits 0-9. The sequence can start with a zero, there’s a 10% chance that it will.]
35-40 years ago I lived with my then young family in the beautiful Thameside town of Marlow, Bucks. Happy days.
Our phone number was 0628 473951, which uses all the digits 0-9 once. I’ve often wondered since, what are the chances of such a thing happening? I invite you to suggest the likelihood of that being a 10-digit number, based on (a) no weighting in relation to the design of UK phone numbers, and (b) the first random selection from a vast and equal number of all the digits 0-9 e.g. 0.5 is a 50% likelihood. I hope and expect that a mathematician / physicist in the Cotswolds – a part of which is sealed off currently for JD Vance‘s visit – will provide the authoritative answer.
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10 to the power of 10, so one in 10 billion.
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Thanks Andy, I’ll reword the clue slightly, may help.
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OK. The first digit can be any digit, so probability 1/1.
Assuming all the digits are unique, the probability of the second digit being different is 9/10.
Continuing, the third being different to the first two is 8/10, giving us the formula
1 / (0.9 x 0.8 x 0.7 x 0.6 x 0.5 x 0.4 x 0.3 x 0.2 x 0.1)
Giving a rounded probability of 1 in 2766.
What say you Mike ?
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I say, “Congratulations, Andy!!!” Put another way, 0.000362 – a chance of 3.62 in 10,000.
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