By Barton G.
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Additional resources for An introduction to Advanced Field Theory
7. 994 40 50 60 EXERCISES 1. Three different classes contain 20, 18, and 25 students, respectively, and no student is a member of more than one class. If a team is to be composed of one student from each of these three classes, in how many different ways can the members of the team be chosen? 2. In how many different ways can the fiv� letters G, b, c, d. and e be arranged? 3. If a man has six different sportshirts and four different pairs of slacks, how many different combinations can he wear? 4.
Arrangements of the n n balls is also n Example 2: Tossing a Coin. Suppose that a fair coin is to be tossed ten times, and it is desired to determine (a) the probability p of obtaining exactly three heads and (b) the probability p ' of obtaining three or fewer heads. (a) The total possible number of different sequences of ten heads and tails is and it may be assumed that each of these sequences is equally probable. The number of these sequences that contain exactly three heads will be equal to the number of different arrangements that can be formed with three heads and seven 210, tails.
In other words, the information that the event B has occulTed is of no help to the person who is trying to decide whether or not the event A has occurred. This matter will be discussed in a more general way in Chapter 2. In the foregoing discussion of independent events, we stated that if A and B are independent, then the occurrence or nonoccurrence of A should not be related to the occurrence or nonoccurrence of B. Hence, if A and B satisfy the mathematical definition of independent events, then it should also be true that A and Be are independent events, that A" and B are independent events, and that AI: and Be are independent events.