Mixing
Probability of guessing password of at least one user out of 500,000, with only 3 attempts on each user
$begingroup$
- 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
asked Jan 17 at 5:14
MatthewMatthew
1084
$endgroup$
add a comment |
$begingroup$
- 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
asked Jan 17 at 5:14
MatthewMatthew
1084
$endgroup$
add a comment |
$begingroup$
- 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
asked Jan 17 at 5:14
MatthewMatthew
1084
$endgroup$
- 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
asked Jan 17 at 5:14
MatthewMatthew
1084
asked Jan 17 at 5:14
MatthewMatthew
1084
asked Jan 17 at 5:14
MatthewMatthew
1084
asked Jan 17 at 5:14
MatthewMatthew
1084
asked Jan 17 at 5:14
MatthewMatthew
1084
1084
add a comment |
add a comment |
1 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 $1-(1-p)^{500,000}approx 0.139$.
answered Jan 17 at 5:27
apsadapsad
1813
$endgroup$
add a comment |
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1 Answer
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1 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 $1-(1-p)^{500,000}approx 0.139$.
answered Jan 17 at 5:27
apsadapsad
1813
$endgroup$
add a comment |
$begingroup$
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 $1-(1-p)^{500,000}approx 0.139$.
answered Jan 17 at 5:27
apsadapsad
1813
$endgroup$
add a comment |
$begingroup$
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 $1-(1-p)^{500,000}approx 0.139$.
answered Jan 17 at 5:27
apsadapsad
1813
$endgroup$
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 $1-(1-p)^{500,000}approx 0.139$.
answered Jan 17 at 5:27
apsadapsad
1813
answered Jan 17 at 5:27
apsadapsad
1813
answered Jan 17 at 5:27
apsadapsad
1813
answered Jan 17 at 5:27
apsadapsad
1813
1813
add a comment |
add a comment |
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