Solution Found!
computer system uses passwords that contain exactly eight
Chapter 2, Problem 141E(choose chapter or problem)
A computer system uses passwords that contain exactly eight characters, and each character is one of the 26 lowercase letters (𝑎-𝑧) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let 𝐴 and 𝐵 denote the events that consist of passwords with only letters or only integers, respectively. Suppose that all passwords in Ω are
equally likely. Determine the following probabilities:
(a) \(P\left(A \backslash B^{\prime}\right))
(b) \(P\left(A^{\prime} \cap B\right)\)
(c) P (password contains exactly 2 integers given that it contains
at least 1 integer)
Equation transcription:
Text transcription:
P(A backslash B^{prime})
P(A^{prime} cap B)
Questions & Answers
QUESTION:
A computer system uses passwords that contain exactly eight characters, and each character is one of the 26 lowercase letters (𝑎-𝑧) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let 𝐴 and 𝐵 denote the events that consist of passwords with only letters or only integers, respectively. Suppose that all passwords in Ω are
equally likely. Determine the following probabilities:
(a) \(P\left(A \backslash B^{\prime}\right))
(b) \(P\left(A^{\prime} \cap B\right)\)
(c) P (password contains exactly 2 integers given that it contains
at least 1 integer)
Equation transcription:
Text transcription:
P(A backslash B^{prime})
P(A^{prime} cap B)
ANSWER:Solution 141E
Step1 of 4:
From the given problem we have:
The number of characteristics contain a password = 8,
Lower case letters = 26,
Upper case letters = 26, and
Integers = 10.
Here our goal is:
a). We need to find
b). We need to find
c). We need to find the probability of password contains exactly 2 integers given that it contains at least 1 integer.
Step2 of 4:
a).
Let us define events are:
A = the event that password consists only letters.
B = the event that password consists only integers.
Now,
The total number of characteristics = 26 + 26 + 10
= 62.
The possible number of 8 digit password = [Because digits are independent to each other]
The number of characteristics in letters = 26 + 26
= 52.
The possible number of 8 digit letters password =
The number of characteristics in Integers = 10
The possible number of 8 digit Integer password =
Conside,
…..(1)
Where,