A transmitter is sending a message by using a binary code, namely, 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 will be 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 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.] c. ?Suppose 70% of all bits sent from the transmitter are 1s. If a 1 is received by the receiver, what is the probability that a 1 was sent?

Answer : Step 1 of 3 : A transmitter is sending a message by using a binary code, namely, 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 will be 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, the claim is to find the probability that a 1 is sent by all three relays. the probability is .20 that the bit sent will be different from the bit received (a reversal). So, the probability of maintaining a bit is 0.8 Using independence, P(all three relays correctly send 1) = (0.8) (0.8) (0.8) = 0.512 the probability that a 1 is sent by all three relays is 0.512.