Answer:
[tex]P(valid) = 1 * 10^{-8}[/tex]
Step-by-step explanation:
Let us first find the number of possible credit card numbers that can be formed with the numbers 0 - 9.
We want to form a 16 digit number out of 10 digits, so, we have:
[tex]N = 10^{16}[/tex]
There are [tex]10^{16}[/tex] numbers that can be formed.
There are only 100 million valid numbers ([tex]100 * 10^6 = 10^8[/tex]). Let the number of valid numbers be n.
Therefore, the probability of picking a number that is valid is:
P(valid) = n / N
[tex]P(valid) = 10^{8} / 10^{16}\\\\P(valid) = 1 * 10^{-8}[/tex]
