6.103 A transmitter is sending a message using a binary code (a sequence of 0’s and 1’s). Each transmitted bit

(0 or 1) must pass through three relays to reach the receiver. At each relay, the probability is .20 that the bit sent on is different from the bit received (a reversal).

Assume that the relays operate independently of one another:

transmitter → relay 1 → relay 2 → relay 3 → receiver

a. If a 1 is sent from the transmitter, what is the probability that a 1 is sent on by all three relays?

b. If a 1 is sent from the transmitter, what is the probability that a 1 is received by the receiver?

(Hint: The eight experimental outcomes can be displayed on a tree diagram with three generations of branches, one generation for each relay.)