Question

A credit 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?

Answer 1

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
`10^(16)`

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
`100*10^(6)=10^(8)`


P (selecting valid)=n(valid)/ n(all) =
`(10^(8))/(10^(16))= (1)/(10^(8))=0.00000001`


Answer: 0.00000001