Mathematics for Computer Science
17.6. Simpson’s Paradox 713 CS 2 men admitted out of 5 candidates 40% 50 women admitted out of 100 candidates 50% EE 70 men admi ...
Chapter 17 Conditional Probability714 This leads us to the conclusion that the admissions gap in not due to any systematic bias ...
17.7. Independence 715 Potential Pitfall Students sometimes get the idea that disjoint events are independent. Theopposite is tr ...
Chapter 17 Conditional Probability716 Deciding when toassumethat events are independent is a tricky business. In practice, there ...
17.8. Mutual Independence 717 independence assumption is not so clear, and the consequences of a faulty assump- tion can be seve ...
Chapter 17 Conditional Probability718 Then these numbers were multiplied to give the probability that a randomly-selected person ...
17.8. Mutual Independence 719 By symmetry, PrŒA 2 çDPrŒA 3 çD1=2as well. Now we can begin checking all the equalities required f ...
Chapter 17 Conditional Probability720 everyone with markerEhas markerA, everyone with markerAhas markerB, everyone with markerBh ...
17.8. Mutual Independence 721 (a)What is the probability that you will get shot if he pulls the trigger? (b)Suppose he pulls the ...
Chapter 17 Conditional Probability722 the revealed card is an Ace. (b)Then calculate Pr KD 2 jE forEequal to each of the f ...
17.8. Mutual Independence 723 Hint:Define the eventsS,F, and “F” as follows: “F”DGuard says Foo-Foo is released FDFoo-Foo is rel ...
Chapter 17 Conditional Probability724 Figure 17.3 The DAGG 0 (c)What is the probability that ! GDG 0? Define the following event ...
17.8. Mutual Independence 725 Figure 17.4 Simple graphG (e) ! G has the property that if it has a directed cycle, then it has a ...
Chapter 17 Conditional Probability726 (b)If at most one of them succeeds, what is the probability that Liz becomes the world fla ...
17.8. Mutual Independence 727 (a)If you have one ace, what is the probability that you have a second ace? (b)If you have the ace ...
Chapter 17 Conditional Probability728 GP:The event that the contestantguesses the door with theprize behind it on his first gues ...
17.8. Mutual Independence 729 Your intuitive judgment about the red deck can be formalized and verified using some inequalities ...
Chapter 17 Conditional Probability730 (c)Prove that, given that the chosen coin came up Heads, the chosen coin is more likely to ...
17.8. Mutual Independence 731 Suppose there was a vaccine to prevent Beaver Fever, but the vaccine was expen- sive or slightly r ...
Chapter 17 Conditional Probability732 are two children in every household and that girls and boys are equally likely to be child ...
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