Question

Chances of the number being a single digit number: 1.8%

Chances of the number being a double digit number: 18.2%

Chances of the number being a triple digit number: 80%

the number is from 0-1,500

Answer 1

We know that between there are 19 single digits number {-9, -8, .....,0, 1, 2, ......, 9}

and 10 of them are between 0-1500 from the above set. So, chances of the digits {0, 1, ....., 9} will be

(0.018*10)/19 = 0.009473684

Now, the case of two digits so there is 180 two digits numbers {-99, -98,..., -11, -10, 10, 11, ...., 98, 99}

and the numbers lie between 0-1500 are {10, 11, ...., 98, 99} . So, the chances will be

0.182*90/180 = 0.091

Now, there are 1800 three digits numbers {-999, -998, ..., -101, -100, 100, 101, ..., 998, 999}

and the numbers lie between 0-1500 are {100, 101,..., 998, 999}. So, the chances will be

0.8*900/1800 = 0.4

and the chances for numbers between 1000-1500 is zero(because total probability is 1 = 0.018+0.182+0.8)

So total chances will be 0.009473684 + 0.091 + 0.4 = 0.5004737

I am including 0 and 1500 to the favourable set. If it is not you can change the solution accordingly.