Mathematics for Computer Science

Introduction Probability is one of the most important disciplines in all of the sciences. It is also one of the least well under ...

Part IV Probability514 that a suspect is guilty given that his blood type matches the blood found at the scene of the crime. Ran ...

16 Events and Probability Spaces 16.1 Let’s Make a Deal In the September 9, 1990 issue ofParademagazine, columnist Marilyn vos S ...

Chapter 16 Events and Probability Spaces516 The car is equally likely to be hidden behind each of the three doors. The player i ...

16.2. The Four Step Method 517 car location A B C Figure 16.1 The first level in a tree diagram for the Monty Hall Problem. The ...

Chapter 16 Events and Probability Spaces518 car location A B C A B C A B C A B C player’s intial guess B A A B A C A C B C C B d ...

16.2. The Four Step Method 519 the host must open door C. However, if the prize is behind door A and the player picks door A, th ...

Chapter 16 Events and Probability Spaces520 car location A B C A B C A B C A B C player’s intial guess B A A B A C A C B C C B d ...

16.2. The Four Step Method 521 car location A B C A B C A B C A B C player’s intial guess B A A B A C A C B C C B door revealed ...

Chapter 16 Events and Probability Spaces522 16.2.3 Step 3: Determine Outcome Probabilities So far we’ve enumerated all the possi ...

16.2. The Four Step Method 523 1 path in 18 should arrive at the.A;A;B/leaf, which is precisely the probability we assign it. We ...

Chapter 16 Events and Probability Spaces524 car location A B C 1=3 1=3 1=3 A B C A B C A B C 1=3 1=3 1=3 1=3 1=3 1=3 1=3 1=3 1=3 ...

16.3. Strange Dice 525 A B C Figure 16.6 The strange dice. The number of pips on each concealed face is the same as the number o ...

Chapter 16 Events and Probability Spaces526 higher,andhe will let you pick a die first, after which he will pick one of the othe ...

16.3. Strange Dice 527 2 6 7 1=3 1=3 1=3 die A 1=3 1=3 1=3 9 1 5 1=3 1=3 1=3 9 1 5 1=3 1=3 1=3 9 1 5 die B winner A B B A A B A ...

Chapter 16 Events and Probability Spaces528 is particularly easy since you just have to compute the number of outcomes in the ev ...

16.3. Strange Dice 529 3 4 8 1=3 1=3 1=3 die C 1=3 1=3 1=3 7 2 6 1=3 1=3 1=3 7 2 6 1=3 1=3 1=3 7 2 6 die A winner C A A C A A C ...

Chapter 16 Events and Probability Spaces530 you do it now, you’ll see by the same reasoning as before thatBbeatsC with probabili ...

16.3. Strange Dice 531 1 st A roll 2 nd A roll sum of A rolls 2 2 7 6 7 7 6 2 2 6 6 7 4 8 9 8 12 13 9 13 14 1 st B roll 2 nd B r ...

Chapter 16 Events and Probability Spaces532 D 1 D 3 D 2 D 1 D 3 D 2 D 1 D 3 D 2 D 1 D 3 D 2 D 1 D 3 D 2 D 1 D 3 D 2 D 1 D 3 D 2 ...