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

Answer 1

Answer:

$P(valid) = 1 * 10^{-8}$

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:

$N = 10^{16}$

There are $10^{16}$ numbers that can be formed.

There are only 100 million valid numbers ($100 * 10^6 = 10^8$). Let the number of valid numbers be n.

Therefore, the probability of picking a number that is valid is:

P(valid) = n / N

$P(valid) = 10^{8} / 10^{16}\\\\P(valid) = 1 * 10^{-8}$