Mathematics for Computer Science
16.4. Set Theory and Probability 533 strangers in bars, it would be a good idea to try figuring out what other relative strength ...
Chapter 16 Events and Probability Spaces534 An immediate consequence of the definition of event probability is that fordis- join ...
16.4. Set Theory and Probability 535 Rule 16.4.4(Union Bound). PrŒE 1 [[EnçPrŒE 1 çCCPrŒEnç: (16.3) This simple Union Bou ...
Chapter 16 Events and Probability Spaces536 1=2 1=2 1=2 1=2 H H H H T T T T 1=2 1=2 1=2 1=2 1=2 1=4 1=8 1= 16 1 st player 1 st 2 ...
16.5. Conditional Probability 537 where Tnstands for a lengthnstring of T’s. The probability function is PrŒTnHçWWD 1 2 nC^1 : T ...
Chapter 16 Events and Probability Spaces538 set of all people in the world set of people who live in Cambridge set of MIT studen ...
16.5. Conditional Probability 539 Pure probability is often counterintuitive, but conditional probability is even worse! Conditi ...
Chapter 16 Events and Probability Spaces540 W W W L L L W L W L 1=2 1=2 2=3 1=3 2=3 1=3 1=3 2=3 1=3 2=3 WW WLW WLL LWW LWL LL ...
16.5. Conditional Probability 541 Step 4: Compute Event Probabilities We can now compute the probability that The Halting Proble ...
Chapter 16 Events and Probability Spaces542 Multiplying edge probabilities in a tree diagram amounts to evaluating the right sid ...
16.5. Conditional Probability 543 yes pos no neg pos neg 0:9 0:1 0:9 0:1 0:3 0:7 0:09 0:01 0:27 0:63 person has BO test ...
Chapter 16 Events and Probability Spaces544 problem is that almost everyone is healthy; therefore, most of the positive results ...
16.5. Conditional Probability 545 makes perfect sense to wonder how likely it is that The Halting Problem won the first game. A ...
Chapter 16 Events and Probability Spaces546 Theorem 16.5.2(Bayes’ Rule).IfPrŒAçandPrŒBçare nonzero, then: Pr BjA D Pr AjB ...
16.5. Conditional Probability 547 16.5.7 Conditioning on a Single Event The probability rules that we derived in Section 16.4.2 ...
Chapter 16 Events and Probability Spaces548 However, the university’s lawyers argued that across the university as a whole, the ...
16.6. Independence 549 CS 0 women granted tenure, 1 candidate 0% 50 men granted tenure, 100 candidate 50% EE 70 women granted te ...
Chapter 16 Events and Probability Spaces550 Definition 16.6.1.An event with probability 0 is defined to be independent of every ...
16.6. Independence 551 There are, of course, many examples of events where assuming independence is notjustified, For example, l ...
Chapter 16 Events and Probability Spaces552 For example, if we tossnfair coins, the tosses are mutually independent iff for ever ...
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