Concept explainers
Keep your password safe: A computer password consists of eight characters. Replications are allowed.
How many different passwords are possible if each character may be any lowercase letter or digit?
How many different passwords are possible if each character may be any lowercase letter?
How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit?
A computer is generating passwords. The computer generates eight characters at random, and each is equally to be any of the 26 letters or 10 digits.
Replications are allowed. is die
A computer system requires that passwords contain at least one digit. If eight characters are generated at random what is the probability that dry will form a valid password?
(a)
To find: the possible passwords having lowercase letter or digit
Answer to Problem 36E
The possible passwords having lowercase letter or digit are,
Explanation of Solution
Given:
Computer password = 8 characters
(A to Z) 26 letters and (0 to 9)10 digits = 36 characters
Calculation:
The possible passwords having lowercase letter or digit are,
Conclusion:
Therefore, the possible passwords having lowercase letter or digit are,
(b)
To find: the possible passwords having lowercase letter
Answer to Problem 36E
The possible passwords having lowercase letter are,
Explanation of Solution
Given:
Computer password = 8 characters
(A to Z) 26 letters and (0 to 9)10 digits = 36 characters
Calculation:
The possible passwords having lowercase letter are,
Conclusion:
Therefore, the possible passwords having lowercase letterare,
(c)
To find: the possible passwords having lowercase letter or digit and should have at least one digit
Answer to Problem 36E
The possible passwords having lowercase letter or digit and should have at least one digit are,
Explanation of Solution
Given:
Computer password = 8 characters
(A to Z) 26 letters and (0 to 9)10 digits = 36 characters
Calculation:
The possible passwords having lowercase letter or digit and should have at least one digit are,
Conclusion:
Therefore, the possible passwords having lowercase letter or digit and should have at least one digit been,
(d)
To find: the probability that password having all letters
Answer to Problem 36E
The probability that passwords having all letters are,
Explanation of Solution
Given:
Computer password = 8 characters
(A to Z) 26 letters and (0 to 9)10 digits = 36 characters
Calculation:
The possible passwords having all letters are, Let
E = the event of getting the password contains all letters.
Conclusion:
The probability that passwords having all letters are,
(e)
To find: the possible passwords having at least one digit
Answer to Problem 36E
The possible passwords having at least one digit are,
Explanation of Solution
Given:
Computer password = 8 characters
(A to Z) 26 letters and (0 to 9)10 digits = 36 characters
Calculation:
The possible passwords having at least one digit are, Let
F = event of getting the password contains at least one digit.
Conclusion:
Therefore, the possible passwords having at least one digit are,
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Chapter 5 Solutions
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
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