Mathematics for Computer Science
16.6. References 693 Now let’s revise our assumptions about how contestants choose doors. Say the doors are labeled A, B, C, and ...
Chapter 16 Events and Probability Spaces694 (d)What is the probability of success ifpis chosen in this way? What quantity does t ...
16.6. References 695 of exactly those components that fail within one year. For example,f2;5gis the outcome that the second and ...
Chapter 16 Events and Probability Spaces696 Problem 16.11. The results of a round robin tournament in which every two people pla ...
17 Conditional Probability 17.1 Monty Hall Confusion Remember how we said that the Monty Hall problem confused even professional ...
Chapter 17 Conditional Probability698 solely of the three outcomes listed in (17.1). In the opening of Section 17.1, we cal- cul ...
17.2. Definition and Notation 699 common one:we chose the wrong condition. In our initial description of the sce- nario, we lear ...
Chapter 17 Conditional Probability700 The O. J. Simpson Trial In an opinion article in theNew York Times, Steven Strogatz points ...
17.3. The Four-Step Method for Conditional Probability 701 local team wins the tournament, given that they win the first game? T ...
Chapter 17 Conditional Probability702 The outcomes in these events are indicated with check marks in the tree diagram in Figure ...
17.4. Why Tree Diagrams Work 703 which is the probability that the local team wins the first game. The second edge is labeled2=3 ...
Chapter 17 Conditional Probability704 Let’s pick some size-ksubset,S Œ1::nç, as a target. Suppose we choose a size-ksubset at r ...
17.4. Why Tree Diagrams Work 705 one of the first lines of defense. They’re not very accurate as far as medical tests go, but th ...
Chapter 17 Conditional Probability706 Step 1: Find the Sample Space The sample space is found with the tree diagram in Figure 17 ...
17.4. Why Tree Diagrams Work 707 notice that there is a simple way to make a test that is 99% accurate: always return a negative ...
Chapter 17 Conditional Probability708 ments and the philosophical meaning of probability. We’ll say a bit more about this after ...
17.4. Why Tree Diagrams Work 709 17.4.6 Philosphy of Probability Let’s try to assign a probability to the event Œ2^6972607 1 is ...
Chapter 17 Conditional Probability710 the probability that 1000 repetitions of the probabilistic test do not discover this is at ...
17.5. The Law of Total Probability 711 This rule extends to any set of disjoint events that make up the entire sample space. For ...
Chapter 17 Conditional Probability712 so Pr AjB D 9 10 DPr AjC : Also, since 0 is the only outcome inB\Cand 0 ...A, we h ...
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