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Statistics / Statistics for Engineers and Scientists 4 / Chapter 2 / Problem 7SE

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

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An electronic message consists of a string of bits (0s and

Chapter 2, Problem 7SE

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QUESTION:

An electronic message consists of a string of bits (0s and 1s). The message must pass through two relays before being received. At each relay the probability is 0.1 that the bit will be reversed before being relayed (i.e., a 1 will be changed to a 0, or a 0 to a 1). Find the probability that the value of a bit received at its final destination is the same as the value of the bit that was sent.

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QUESTION:

An electronic message consists of a string of bits (0s and 1s). The message must pass through two relays before being received. At each relay the probability is 0.1 that the bit will be reversed before being relayed (i.e., a 1 will be changed to a 0, or a 0 to a 1). Find the probability that the value of a bit received at its final destination is the same as the value of the bit that was sent.

ANSWER:

Answer

Step 1 of 2

Given that an electronic message consists of bits 0 and 1

The message must pass through two relays before being processed

The probability of bit being reversed before reaching each relay is 0.1

The probability of bit being reversed =0.1+0.1

=0.2

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