A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If a number is entered randomly, what is the probability that it is a valid number?

There are ${\displaystyle {10}^{16}}$ strings of 16 digits between 0 and 9 (for each of the 16 digits we have 10 choices). Also, 100 million = ${\displaystyle 100\cdot {10}^6={10}^8}$. So, the probability that the random entered number is valid is
number of valid numbers/all strings of 16 digits=${\displaystyle \frac{{10}^8}{{10}^{16}}=\frac{1}{{10}^8}}$
which is almost zero.