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

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): You can put this solution on YOUR website!

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.
RELATED QUESTIONS
A computer password is to be made up consisting of four alphabetical characters. How many (answered by Fombitz,Alan3354)

A password for a computer account must contain five characters, and letters and digits... (answered by Fombitz)

On a certain computer network each user has to have a password consisting of six to... (answered by Edwin McCravy)

Please help me this problem is driving me crazy. I need to know what equation do I use. (answered by Edwin McCravy)

Please help me I never did a problem like this. Show all steps A computer password (answered by stanbon)

A computer requires eight characters for a password. The first character must be a letter (answered by richard1234)

A computer password is to consist of four alphanumeric characters with no repeats. How... (answered by ewatrrr)

each user on a computer system has a password which can be 5 to 7 characters long, where... (answered by edjones)

A computer password consists of 4 characters. The characters can be one of the 26 letters (answered by Edwin McCravy)