Discrete Math 12.2.5: Probability a random string is a valid password. An online

Question

Discrete Math

12.2.5: Probability a random string is a valid password.

An online vendor requires that customers select a password that is a sequence of upper-case letters, lower-case letters and digits. A valid password must be at least 10 characters long, and it must contain at least one character from each of the three sets of characters. What is the probability that a randomly selected string with exactly ten characters results in a valid password? The alphabet for the strings in the sample space from which the string is drawn is the union of the three sets of characters.

Explanation / Answer

The numer of letters is 26, Now upper case will be 26 and lower case will be 26.

Total number of digits are 10

And the password needs to be 10 character long

The probability of valid password will be (26+26+10)10 - 2610- 2610- 1010

we have deleted the passwords probability with all letters or all digits

= 6210- 2610- 2610- 1010

= 8.0101 * 1017

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