Superior Security recently discovered a computer on its network had be

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Competition Mode Question

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)  \frac{52!}{16!36!}

(B)  \frac{1}{\frac{62!}{16!46!}}

(C)  \frac{1}{\frac{52!}{16!36!}}

(D)  \frac{1}{52^{16}}

(E)  \frac{1}{62^{16}}

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madgmat2019 · Answer

Since its in a first try.....it should be unique......so its '1'

total no.of possiblities is numbers(0-9), letters(26)..its becomes 52(both lower-case and upper-case letters)....Total=62
so the probability is 1/62 for each of 16 numbers.....
total probability- 1/(62)^16

OA:E

Archit3110 · Answer

total alphabets = 26 
lower + upper = 26+26 ; 52
total nos= 0-10 ; 10
so total possible characters for 16 digit password = 62
and P of getting in first try= 1/62^16
IMO E

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!52!16!36!

(B) 162!16!46!162!16!46!

(C) 152!16!36!152!16!36!

(D) 1521615216

(E) 1/62^16

exc4libur · Answer

A to Z = 26 upper letters 
a to z = 26 lower letters 
0 to 9 = 10 digits
Total chars = 52+10 = 62
Password = 16 chars
Probability = 1 / (62)^{16}

Ans (E)

vinkumar29 · Answer

1. Hacker knows that the password includes digits from 0-9 and both UPPER CASE and lower case letters. So, the total number of letters/digits to chose from is 10+ 26+ 26 = 62.
2. Total possible ways of choosing a password from 62 letters/digits is 62C16 which is 62!/ = 62!/(16!*46!)
3. There is only 1 possible way of choosing the right password, therefore the probability of choosing the right password is 
 1/  which is the option B.

freedom128 · Answer

It doesn't say the numbers/upper-case letters/lower-case letters can only be used once. So, there should be 62 possibilities for each of 16 characters.

FINAL ANSWER IS (E) 1/(62^16)

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lacktutor · Answer

If guessing on the first try of 16 characters password is right, the probability will be  \frac{1}{n^{16}}  ( the repetition is allowed)

10(numbers) + 26( lower case letters) + 26( upper case letters) = 62( characters)

In total, 62 characters could be used in each of 16 characters: 
—>  62*62*...* 62 = 62^{16} 
—> the probability =  \frac{1}{62^{16}}

The answer is E.

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eakabuah · Answer

Total possible combinations = 26 upper case letters (A to Z) + 26 lower case letters (a to z) + 10 numbers (0 to 9)
= 62.
The password is 16 digits long, hence the total number of possible combinations = 62^16
Probability of guessing right on the first try = 1/62^16

The answer is E in my view.

Bunuel · Answer

OFFICIAL EXPLANATION

1. The probability of guessing correctly on the first try is 1 divided by the number of pass permutations (i.e., unique arrangements of passwords). For example, if there were four possible password combinations, the probability of guessing the password correctly on the first try would be 1/4

2. For each of the 16 characters that form the password, the possible characters include: 26 lower case characters, 26 upper case characters, and 10 digits. So, for each character in the password, there are 62 possible characters.
Character 1 Character 2 Character 3 ... Character 15 Character 16
62 possibilities 62 possibilities 62 possibilities 62 possibilities 62 possibilities 62 possibilities

3. Since there are 16 characters in the password and each character could be one of 62 possibilities, there are a total of 62^16 unique password permutations (i.e., there are 62^16 different possible passwords, only one of which is the correct password). So, the probability of guessing the password on the first try is 1/62^16.

ScottTargetTestPrep · Answer

Since there are 10 one-digit numbers, 26 lower-case letters, and 26 upper-case letters, the probability that the password was correctly guessed on the first try is 1/(10 + 26 + 26)^16 = 1/62^16

Answer: E

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Superior Security recently discovered a computer on its network had be

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