7. A sequence of binary digits (0's and 1's) representing the outcome of a se- quence of fair coin tosses ("Heads" and "Tails", respectively) is sent through a noisy communications channel, in which digits are received as sent only 95% of the time. In order to improve reliability, each digit in a message is sent three times. For instance, the sequence 1001... would be sent as 111000000111... through the channel (but might be received as, e.g., 111010110101...). Sup- pose that the first 3 digits received are 111. Show that, given this, the first toss was indeed "Tails" with conditional probability 99.99%.

7. A sequence of binary digits (0's and 1's) representing the outcome of a se- quence of fair coin tosses ("Heads" and "Tails", respectively) is sent through a noisy communications channel, in which digits are received as sent only 95% of the time. In order to improve reliability, each digit in a message is sent three times. For instance, the sequence 1001... would be sent as 111000000111... through the channel (but might be received as, e.g., 111010110101...). Sup- pose that the first 3 digits received are 111. Show that, given this, the first toss was indeed "Tails" with conditional probability 99.99%.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.CT: Chapter Test

Problem 3CT: An Internet service provider requires its customer to select a password consisting of four letters...

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