Discrete Mathematics for Computer Science

Ideas of Chance in Computer Science 477 set of possible results that we can enumerate. However, the result that will actually oc ...

478 CHAPTER^8 Discrete Probability we believe that the 36 outcomes are equally likely, we choose p(co) to be 1/36 for each (0 E ...

Ideas of Chance in Computer Science 479 Example 2. Suppose Q2 = {0, 1}. Then, 0 and 1 are the outcomes. Here, 0 might represent ...

480 CHAPTER 8 Discrete Probability If E = 0, there are no terms in the sum, and P (0) is 0. Example 4. For the sample space { 1, ...

Ideas of Chance in Computer Science 481 obtaining a sum of 3 is both an outcome and a one-element event E = {3}. Suppose, now, t ...

(^482) CHAPTER 8 Discrete Probability How to Calculate the Probability of Events Describe in words the experiment and the event ...

Ideas of Chance in Computer Science 483 are assumed to be fair, meaning that each card of a deck, face of a coin, or side of a d ...

484 CHAPTER 8 Discrete Probability Example 9. Suppose the analysis of a sorting algorithm shows that the worst case (the one req ...

Ideas of Chance in Computer Science 485 introduced in Section 1.3 also help in computing the probability of events (with or with ...

486 CHAPTER 8 Discrete Probability (b) Since E is the disjoint union of (E N) F) and (E n F), the Additive Principle implies sta ...

Ideas of Chance in Computer Science 487 Proof Since 0 = E U E expresses Q as a union of disjoint sets, P(Q) = P(E) + P(E) Since ...

488 CHAPTER 8 Discrete Probability Now that we have derived an expression for P(E), how do we evaluate it? Trying to compute n! ...

Exercises 489 w0 p1 (w0) P2 (W0) Woi -1/2 1/31f7 (02 1/4 2/31/7- W03 1/4 1/3/7 a04 1/2 2/3/7 (05 1/2 (,/7--2)/17 Two nickels an ...

490 CHAPTER 8 Discrete Probability For the two nickels and the dime in Exercise 8, there are eight possible combinations of hea ...

Cross Product Sample Spaces 491 15. Suppose A and B are events in a sample space such that P(A) = 1/4, P(B) = 5/8, and P(A U B) ...

492 CHAPTER^8 Discrete Probability detail situations like repeated coin flipping, and we explain how to view events in separate ...

Cross Product Sample Spaces 493 should be (0.7) (0.4) = 0.28. Continuing in this way, we assign to each ordered pair of out- com ...

494 CHAPTER 8 Discrete Probability On the other hand, we can reason as follows: The probability that a person has a particular b ...

Cross Product Sample Spaces 495 where w ranges over the outcomes (W0, w2) in 92. By definition of p, the left-hand side is YE (p ...

496 CHAPTER 8 Discrete Probability where si E Si for i > 1. Note that the size of a cross product of finitely many finite set ...