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Credit card numbers are not randomly generated. The first few digits identify the card issuing company. The second digit of a card issued by American Express must be 4 or 7. With Diners Club and Carte Blanche, the second digit must be 0, 6 or 8. So the probability of the second digit being a 3 is 0 for two of the major issuers. Other card issuers have different starting sequences so you would need to know these rules. Furthermore, you cannot assume that all cards starting with a certain sequence have actually been issued. Going back to the Diners Club, example, you would need to know how many of the n0, n6 and n8 cards were actually issued. In short, searching for an answer to the question is futile.

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Q: What is the probability the second digit of the credit card number is a 3?
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