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
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asked 2020-10-20
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?

Answers (1)

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.
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