Name: 10 points Question 3 A transmitter is sending a message by using a binary

Question

Name: 10 points Question 3 A transmitter is sending a message by using a binary code, namely, a sequence of O's and I's. Each transmitted bit (0 or 1) must pass through three relays (also known as repeaters). At each relay, the probability is 0.2 that the bit will be different from the bit received (a reversal). Assume that the relays operate independently of one another. Transmitter Relay1Relay2 - Relay3Receiver (5 points) (a) If a 1 is sent from the transmitter, what is the probability that a 1 is sent by all three relays? points) (b) Suppose 70% of all the bits sent from the transmitter are is. If a 1 is received by the receiver, what is the probability that a 1 was sent?

Explanation / Answer

P(differing)=0.2
P(not differing)=0.8

a)
None of the relays differ
p=0.8*0.8*0.8=0.512

b)
In two different way, this can be possible.
First one is none of the relays differ whose probability is 0.512
The second one is any of the two relays among three will differ and one relay gives output unaltered whose probability is 3*0.2*0.2*0.8=0.096

Required probability=0.512+0.096=0.608

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