Franco is solving a system of linear equations algebraically. He find that there
1 answer:
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Answer:
0,008 or 0,8%
Step-by-step explanation:
To calculate the probability the selected password is made out only of lower-case letters, if it's only letters, we have first to find out how many passwords could be formed with only letters and with only lower-case letters.
For lowercase letters, we can make this many passwords, since for each of the 7 characters, we can pick among 26 lowercase letters:
NLL = 26 * 26 * 26 * 26 * 26 * 26 * 26
In the same fashion, for the number of passwords consisting only of letters, we can pick among 52 letters for each each character (26 lower-case, 26 upper-case):
NOL = 52 * 52 * 52 * 52 * 52 * 52 * 52
We can rewrite NOL differently to ease our calculations:
NOL = (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26)
or
NOL = 26 * 26 * 26 * 26 * 26 * 26 * 26 * 2 * 2 * 2 * 2 * 2 * 2 * 2
Now we have to find out the probability a password containing only letters (NOL) is a password containing only lowercase letters (NLL). So, we divide NLL by NOL:
The probability is thus 1/2^7 or 1/128 or 0,0078125
Which we are asked to round to 3 decimals... so 0,008 or 0,8%