Mathematics for Computer Science

16.6. Independence 553  1 person in 40 has markerC.  1 person in 5 has markerD.  1 person in 170 has markerE. Then these numb ...

Chapter 16 Events and Probability Spaces554 By symmetry, PrŒA 2 çDPrŒA 3 çD1=2as well. Now we can begin checking all the equalit ...

16.7. The Birthday Principle 555 everyone with markerEhas markerA, everyone with markerAhas markerB, everyone with markerBhas ma ...

Chapter 16 Events and Probability Spaces556 Selecting a sequence ofnstudents for a class yields a sequence ofnbirthdays. Under t ...

16.7. The Birthday Principle 557 1/.d2/


.d.n1//lengthnsequences of distinct birthdays. So the proba- bility that everyone has ...

Chapter 16 Events and Probability Spaces558 Problems for Section 16.2 Exam Problems Problem 16.1. (a)What’s the probability that ...

16.7. The Birthday Principle 559 (a)What is PrŒGPç?.... Pr  OP ˇ ˇGP?. (b)What is PrŒOPç? (c)LetRbe the number of times the ga ...

Chapter 16 Events and Probability Spaces560 P.x;y/WWD8z: E.x;z/ORE.y;z/ P.x;y/WWD8z: x¤yIMPLIES ŒE.x;z/ORE.y;z/ç For the follo ...

16.7. The Birthday Principle 561 Answer the questions below using the four step method. You can use the same tree diagram for al ...

Chapter 16 Events and Probability Spaces562 equation insand then solve. Homework Problems Problem 16.7. [The Four-Door Deal] Let ...

16.7. The Birthday Principle 563 Problem 16.8. I have a deck of 52 regular playing cards, 26 red, 26 black, randomly shuffled. T ...

Chapter 16 Events and Probability Spaces564 We may as well assumep < 1=n, since the upper bound is trivial otherwise. For exa ...

16.7. The Birthday Principle 565 be an event such that PrŒBç > 0. Define a function PrBf
gon outcomesw 2 Sby the rule: PrBf!g ...

Chapter 16 Events and Probability Spaces566 events RWWDRed deck is in the box; BWWDBlue deck is in the box; EWWDEight of hearts ...

16.7. The Birthday Principle 567 picked the complete deck, given that you selected the eight of hearts? Use the four-step method ...

Chapter 16 Events and Probability Spaces568 the assigned problems contain errors. If you ask a Teaching Assistant (TA) whether a ...

16.7. The Birthday Principle 569 Remarkably, the two answers are different. This problem will test your counting ability! Proble ...

Chapter 16 Events and Probability Spaces570 Problems for Section 16.6 Exam Problems Problem 16.22. Sally Smart just graduated fr ...

16.7. The Birthday Principle 571 (e)Show that the event that Sally Smart attends MITisindependent of the event that she is happy ...

Chapter 16 Events and Probability Spaces572 is less than the probability for a man. That is, Pr  AjFEE  <Pr  AjMEE  and ( ...