Probability of guessing password of at least one user out of 500,000, with only 3 attempts on each user












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  • There are 500,000 users

  • Every user's password is exactly 7 digits (0-9)

  • After 3 attempts the account is locked.


The probability of guessing any particular user's password would be 3/10,000,000, but how would I calculate the probability that an attacker could gain access to at least one account?






probability







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$endgroup$

















    1












    $begingroup$



    • There are 500,000 users

    • Every user's password is exactly 7 digits (0-9)

    • After 3 attempts the account is locked.


    The probability of guessing any particular user's password would be 3/10,000,000, but how would I calculate the probability that an attacker could gain access to at least one account?






    probability







    share|cite|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$



      • There are 500,000 users

      • Every user's password is exactly 7 digits (0-9)

      • After 3 attempts the account is locked.


      The probability of guessing any particular user's password would be 3/10,000,000, but how would I calculate the probability that an attacker could gain access to at least one account?






      probability







      share|cite|improve this question









      $endgroup$





      • There are 500,000 users

      • Every user's password is exactly 7 digits (0-9)

      • After 3 attempts the account is locked.


      The probability of guessing any particular user's password would be 3/10,000,000, but how would I calculate the probability that an attacker could gain access to at least one account?






      probability




      probability






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 17 at 5:14









      MatthewMatthew

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      1084






















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          $begingroup$

          Let $p=3/10^7$ be probability of guessing the password for user $i$.



          Assuming you are truly guessing (that is, you are simply punching in random digits), the probability you do not guess the password for user $i$ is $1-p$. Thus, the probability you do not guess password for any user is $(1-p)^{500,000}$ (these are just independent events). Thus probability you guess password for at least one user is $1-(1-p)^{500,000}approx 0.139$.






          share|cite|improve this answer









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            $begingroup$

            Let $p=3/10^7$ be probability of guessing the password for user $i$.



            Assuming you are truly guessing (that is, you are simply punching in random digits), the probability you do not guess the password for user $i$ is $1-p$. Thus, the probability you do not guess password for any user is $(1-p)^{500,000}$ (these are just independent events). Thus probability you guess password for at least one user is $1-(1-p)^{500,000}approx 0.139$.






            share|cite|improve this answer









            $endgroup$


















              2












              $begingroup$

              Let $p=3/10^7$ be probability of guessing the password for user $i$.



              Assuming you are truly guessing (that is, you are simply punching in random digits), the probability you do not guess the password for user $i$ is $1-p$. Thus, the probability you do not guess password for any user is $(1-p)^{500,000}$ (these are just independent events). Thus probability you guess password for at least one user is $1-(1-p)^{500,000}approx 0.139$.






              share|cite|improve this answer









              $endgroup$
















                2












                2








                2





                $begingroup$

                Let $p=3/10^7$ be probability of guessing the password for user $i$.



                Assuming you are truly guessing (that is, you are simply punching in random digits), the probability you do not guess the password for user $i$ is $1-p$. Thus, the probability you do not guess password for any user is $(1-p)^{500,000}$ (these are just independent events). Thus probability you guess password for at least one user is $1-(1-p)^{500,000}approx 0.139$.






                share|cite|improve this answer









                $endgroup$



                Let $p=3/10^7$ be probability of guessing the password for user $i$.



                Assuming you are truly guessing (that is, you are simply punching in random digits), the probability you do not guess the password for user $i$ is $1-p$. Thus, the probability you do not guess password for any user is $(1-p)^{500,000}$ (these are just independent events). Thus probability you guess password for at least one user is $1-(1-p)^{500,000}approx 0.139$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Jan 17 at 5:27









                apsadapsad

                1813




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