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Superior INSecurity Probability

Expert replies
by GmatKiss » Fri Oct 28, 2011 1:37 pm
Superior Security recently discovered a computer on its network had been hacked. The computer password contained 16 characters (including only numbers and letters). What is the probability that the password to Superior's hacked computer was correctly guessed on the first try? (Assume that the hacker knew the password contained 16 characters, comprised only of numbers and both lower-case and upper-case letters.)

A) 52!/(16!36!)
B) 1/[62!/(16!46!)]
C) 1/[52!/(16!36!)]
D) 1/5216
E) 1/6216
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Source: — Problem Solving |

by user123321 » Fri Oct 28, 2011 4:08 pm
GmatKiss wrote:Superior Security recently discovered a computer on its network had been hacked. The computer password contained 16 characters (including only numbers and letters). What is the probability that the password to Superior's hacked computer was correctly guessed on the first try? (Assume that the hacker knew the password contained 16 characters, comprised only of numbers and both lower-case and upper-case letters.)

A) 52!/(16!36!)
B) 1/[62!/(16!46!)]
C) 1/[52!/(16!36!)]
D) 1/5216
E) 1/6216
if characters can be repeated then
1/(26+26+10)^16
if characters are not repeated then
1/62p16

I am not so sure about those options. what is OA?

user123321
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Want to do it right the first time.
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by shankar.ashwin » Fri Oct 28, 2011 7:19 pm
26 - lower cases
26 - upper cases
10 - numbers
Total - 62.

Its a password, hence repetition should be allowed.
Each of the 16 characters could take any any of the 62 possibilities.

Hence we have 1/(62^16)
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