2 Elsa is creating a new FB account, and doesn't know what to make h password. She decides to generate a 14-character password by sele independently and uniformly at random from {a, b, ..., z} U {A, B, . Characters can be repeated. (a) What is the probability that exactly 7 of the characters are dig (b) What is the expected number of digits in the password? (c) What is the variance of the number of digits in the password?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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3 Elsa is creating a new FB account, and doesn't know what to make her
password. She decides to generate a 14-character password by selecting each character
independently and uniformly at random from {a, b, . . . ,
Characters can be repeated.
z} U {A, B, ..., Z} U {0, 1, ..., 9}.
(a) What is the probability that exactly 7 of the characters are digits?
(b) What is the expected number of digits in the password?
(c) What is the variance of the number of digits in the password?
Transcribed Image Text:3 Elsa is creating a new FB account, and doesn't know what to make her password. She decides to generate a 14-character password by selecting each character independently and uniformly at random from {a, b, . . . , Characters can be repeated. z} U {A, B, ..., Z} U {0, 1, ..., 9}. (a) What is the probability that exactly 7 of the characters are digits? (b) What is the expected number of digits in the password? (c) What is the variance of the number of digits in the password?
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