Acredit card contains 16 digits between 0 and 9. how- ever, only 100 million numbers are valid. if a number is entered randomly, what is the probability that it is a valid number?

The total number of 16-digit numbers we can form with the digits 0, 1, ...9 , with

0 allowed to be the first digit, is  

because any of the 16 digits can be one of {0, 1, 2, ...9}, and can be combined with the 15 others, each of which have also 10 possibilities.

100 million is 

P (selecting valid)=n(valid)/ n(all) = 

0.00000001