If a pair of dice is tossed, find the probability of the following events: 1. Two even numbers showing 2. A sum less than 8 3. An odd sum showing 4. The two numbers differ by 2 or less. Problem 3: In a digital communication system which transmits 1's and 0's the probability of a 0 being transmitted is 0.45 and the probability of a 1 being transmitted is 0.55. Because of noise in the system, sometimes a bit is detected wrong. Let the probability of a transmitted 0 being received as a 1 be 0.1 and the probability of a transmitted 1 being received as a 0 be 0.04. 1. If a 0 is received, what is the probability that that bit was sent as a 0? 2. If a l is received, what is the probability that that bit was sent as a 1? 3. In a very long message, what fraction of the bits is received wrong?