# 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?

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