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%.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

8(14-9)+5 32+6
W+7/8=6
7 3 -4 1 -1 0 0 0 1 -2 1 3 7. 1
37in 2o00
4 7 1 k 3.
19 a-c
4 3/6+2 2/8=
6 -2 -2 10 -3 5 1 ---3-0 A = C -10 1 B . 5 || 2 9 4 4 7 0 0 11 <-2 a = 1, b = [3 0 8].