SOLUTION: A computer is generating passwords. The computer generates eight characters at random, and each is equally likely to be any of the 26 letters or 10 digits. Replications are allowe
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Question 1022631: A computer is generating passwords. The computer generates eight characters at random, and each is equally likely to be any of the 26 letters or 10 digits. Replications are allowed. What is the probability that the password will contain all letters? Answer by mathmate(429) (Show Source):
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Question:
A computer is generating passwords. The computer generates eight characters at random, and each is equally likely to be any of the 26 letters or 10 digits. Replications are allowed. What is the probability that the password will contain all letters?
Solution:
There are 26+10=36 possible choices for each digit.
There are 8 digits.
For letters only, there are only 26 choices (assuming upper and lower cases are interchangeable).
No. of letters-only arrangements = 26^8 = 208827064576
No. of alphanumeric arrangements = 36^8 = 2821109907456
Probability of letters-only arrangements =
= 0.07402 (approx.)
On the other hand, if upper and lower cases are assumed distinct letters (as in most computer systems), then there are 26+26+10=62 alphameric choices, and 52 alphabetic choices.
The corresponding probability (letters only) is then
=
=
= 0.24484 (approximately)
which is considerably higher.
