Question

A computer is generating passwords. The computer generates six characters at random, and each is equally likely to be any of the letters or digits. Replications are allowed. What is the probability that the password will contain all letters?

Answer 1

The probability of all letters arrangement if the upper cases and the lower cases of the English alphabet are interchangeable = 14.2%

The probability of all letters arrangement if the upper cases and the lower cases are not interchangeable = 34.8%

Explanation:

please kindly check the attached files for explanation.

Answer 2

0.1419 ( (if upper and lower cases are interchangeable)

0.348 ( if upper and lower cases are distinct letters)

Explanation:

Each digit has 36 possible choices as 26+10

computer generates six characters

there are only 26 choices for letters only, (if we assume upper and lower cases are interchangeable)

For number of letters-only arrangements =
`26^(6)` = 308915776

For number of alphanumeric arrangements =
`36^(6)`= 2176782336

In order to find the probability of letters-only arrangements :
`(308915776)/(2176782336)`

=>0.1419

Now, in different scenario if upper and lower cases are not interchangeable.

We will have 26+26+10=62 alphanumeric choices, and 52 alphabetic choices

Therefore, probability of letters-only arrangements will be
`(52^(6) )/(62^(6) )`

=>0.348