1. North and South have all the aces between them in a bridge game. What is the probability that one has one ace and the other has three?
2. Three independent proofreaders will read a manuscript. The prob- abilities that a particular error will be detected by them are respectively :92; :85, and :95. What is the probability that the error will go undetected?
3. * Two numbers are chosen without replacement from 1; 2; : : : 100. What is the probability that the smaller number is greater than 20 if the larger num- ber is smaller than 60?
4. Sam, Fred, and Vishy in that order take turns shooting at a bull's eye. Their success rates are20%; 30%, and 40%. What are the probabilities of each making the first hit at the bull's eye?
5. (Communication Channel). A signal passes through three filtering networks. The signal can be a C signal or a - signal. Each network has a probability p of transmitting the signal as it was received and probability 1 - p of transmitting it as the wrong signal. Assume that the networks function independently. If a signal is received as a C, what is the probability that it was sent as a C? You may assume that the prior probability is 50% that it was sent as a C.