A computer system uses passwords that contain exactly 5 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 ? 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 ? are equally likely. Determine the following probabilities. a. P(A|B′) = b. P(A′ ∩ B′) = c. The probability that password contains exactly 2 integers given that it contains at least 1 integer. P =

A computer system uses passwords that contain exactly 5 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 ? 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 ? are equally likely. Determine the following probabilities. a. P(A|B′) = b. P(A′ ∩ B′) = c. The probability that password contains exactly 2 integers given that it contains at least 1 integer. P =

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.2: Probability

Problem 31E

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