Question

# 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?

Complex numbers
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?

2020-10-21
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.