Mathematics for Computer Science
16.2. The Four Step Method 673 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 Spaces674 16.2.3 Step 3: Determine Outcome Probabilities So far we’ve enumerated all the possi ...
16.2. The Four Step Method 675 chance it would follow theB-branch at the third level. Thus, there is half of a one third of a on ...
Chapter 16 Events and Probability Spaces676 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 677 16.2.5 An Alternative Interpretation of the Monty Hall Problem Was Marilyn really right? Our analysis ind ...
Chapter 16 Events and Probability Spaces678 A B C Figure 16.6 The strange dice. The number of pips on each concealed face is the ...
16.3. Strange Dice 679 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 Spaces680 Step 4: Compute event probabilities. The probability of an event is the sum of the p ...
16.3. Strange Dice 681 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 Spaces682 dude picksAorB, the odds would be in your favor this time. Biker dude must really be ...
16.3. Strange Dice 683 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 Spaces684 How can it be thatAis more likely thanBto win with one roll, butBis more likely to w ...
16.4. The Birthday Principle 685 16.4.1 Exact Formula for Match Probability There arednsequences ofnbirthdays, and under our ass ...
Chapter 16 Events and Probability Spaces686 a small fraction ofd. The Birthday Principle also famously comes into play as the ba ...
16.5. Set Theory and Probability 687 An immediate consequence of the definition of event probability is that fordis- jointevents ...
Chapter 16 Events and Probability Spaces688 Rule 16.5.4(Union Bound). PrŒE 1 [[En[çPrŒE 1 çCCPrŒEnçC: (16.6) The Un ...
16.5. Set Theory and Probability 689 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 nd pla ...
Chapter 16 Events and Probability Spaces690 whereTnstands for a lengthnstring ofT’s. The probability function is PrŒTnHçWWD 1 2 ...
16.6. References 691 p^1 n 4. q 2 n Exam Problems Problem 16.2. (a)What’s the probability that 0 doesn’t appear amongkdigits ...
Chapter 16 Events and Probability Spaces692 are a Head and then a Tail, the first player wins. If the flips are a Tail and then ...
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