Identify Theft with Credit Cards. Credit card numbers typicallyhave 16 digits, b

Question

Identify Theft with Credit Cards. Credit card numbers typicallyhave 16 digits, but not all of them are random. Answer thefollowing and express probabilities as fractions.
  Discover cards begin with the digits 6011. If youknow the last four digits of a Discover card, what is theprobability of randomly generating the other digits and getting allof them correct? Is this something to worry about?
  Discover cards begin with the digits 6011. If youknow the last four digits of a Discover card, what is theprobability of randomly generating the other digits and getting allof them correct? Is this something to worry about?

Explanation / Answer

So you know 8 of the numbers already. Now you justcalculate the odds of getting the other 8 right. There are 10 choices for each digit:0,1,2,3,4,5,6,7,8,and9 There is a 1 in 10 chance (1/10) of getting the rightdigit. To get 8 digits right in a row, the answer is:(1/10)(1/10)(1/10)(1/10)(1/10)(1/10)(1/10)(1/10) or (1/10)8 which equals .00000001chance. I would say it isn't something to worry about.

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