Question: Consider the communication system described here. The transmitter throws one of two fair dice, die I if the message is A and die II if the message is B. Die I has five faces labeled A and one face labeled B, whereas die II has five faces labeled Band one face labeled A. The receiver decides the message is that shown by the thrown die. Assume the two messages are equally likely,
a. Construct a suitable probability system and determine the probability of error (i.e., the probability that the receiver's decision is incorrect).
b. Now assume that the transmitter throws three type I dice if the message IS A and three type IIdice If the message is B. The receiver decides the message by majority rule. Repeat part a."
c. What is the general expression for the probability of error when the transmitter throws N (N odd) type I or type II dice and the receiver decides by majority rule?
d. The transmitter now throws four type four type II dice. The receiver again decides by majority rule but asks the transmitter to throw the same four dice again in case of a tie. This continues until a decision is reached. What is the probability of error? What is the probability that the decision will be reached with the Nth repetition?