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Answer: 1 / 999,999,999
Explanation:
You can do it in two different ways.
1) First approach
probability = number of positive events / number of possible events
i) number of positive events = 1 (your number is just one number)
ii) number of possible events = number of valid numbers
Assuming the smallest valid number is 1, and the greatest one is 999,999,999, that leads to 999,999,999 different numbers
iii) probability = 1 / 999,999,999
2) Second approach
i) there are 9 digits.
ii) the guesser must guess all the digits in the correct order
iii) since there are 10 digits, from 0 to 9, there are 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1,000,000,000 different combinations
But that includes the number 000,000,000 which is not valid, so you have to subtract 1: 1,000,000,000 - 1 = 999,999,999
Which leads to the same result of the first approach.