Guidance and Instructions The followings are a few points that you should keep in mind as you go through the course. . The set of all possible outcomes of an experiment is called the sample space of the experiment and will be denoted by S. . A subset of a sample space of S for an experiments is called an event. If an outcome x is in A we write YEA. . If the sample space S of an experiment consists of N = \\S| outcomes that are equally likely to oc- cur, then the probability of each outcome is 1/N. If N(E) = [E| denotes the number of outcomes consti- tuting the event E, then the probability of E is P(E) = N(E) N . For conditional probability of B, given that A has already occurred, we have P(B | A) = P(AnB) P(A) for P(A) # 0. Exercise 1: Events, Counting, and Probabilities (i) Resistors manufactured by a machine produc- ing 10 resistors are unacceptable if they are not within 500 of the nominal value. Four such resis- tors are tested. (a) Describe the sample space S of this experiment. (b) Denote by E, the event that ith resistor tests ac- ceptable. Are Eis mutually exclusive? (c) Find E1 n E2, E1 U E2, and Ef. (d) Find (E1 UE2) n E3. (e) Find E1 n E2 ( E3 n E4 and E1 U E2 U E3 U E4. (f) Find (E, U E2 U E3 UE,) = S - (E] UE2 U E3 UE,)