Section 4.4 Events of Length Variable

4.4 Events of Variable Length 2 “Cereal Prizes” To increase sales for Sugar Munchies you put a letter W, I, or N in each box. When kids have all 3 letters they turn them in for a prize. “W” appears on 50% of all tickets “I” appears on 40% of all tickets “N” appears on 10% of all tickets Examples: What would be an important question to ask?

4.4 Events of Variable Length 3 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

4.4 Events of Variable Length 4 “1 - 1 Free Throw Shooting” Every time Morgan shoots he has a 60% chance of making a basket. He has a “1 and 1” free-throw. If he misses the first shot he is done. If he makes the first shot he gets to try a second shot. Which is most likely—Morgan will score 1. 0 Points 2. 1 Point 3. 2 Points

4.4 Events of Variable Length 5 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Correct answer Vote

4.4 Events of Variable Length 6 “Grasshopper” A grasshopper sits in the middle of a 4 foot log Each minute it is equally likely to hop 1 foot to the left or to the right. If it lands on either end of the log it falls off. How long will the grasshopper stay on the log? Examples Animation

4.4 Events of Variable Length 7 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

4.4 Events of Variable Length 8 “Scratch-Off Tickets” A market has a “Scratch-off tickets” contest. There are 1000’s of tickets. Most simply say “Sorry–Try again”. But 10 say $ say $ say $50 40 say $25 If customers get one of these tickets, they sign their name on it and put it in a bucket. At the end of the week the manager draws names and gives prizes until the total dollars first reach (or exceed) $500 How many winners do you expect to have each week?

4.4 Events of Variable Length 9 1. Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

4.4 Events of Variable Length 10 “Baseball Divisional Series” A is playing B. The first team to win 3 games wins the divisional series. Here are some ways the Series can end: Suppose that team A has a 55% chance of winning any single game. What are the chances that A will win the series?

4.4 Events of Variable Length Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

4.4 Events of Variable Length 12 “Baseball Simulation” Suppose that a modified baseball game consists of three bases (including home plate). There are still 3 outs in an inning. Examples: The chances that a batter makes single (one base) = 0.3 double (two bases) = 0.2 home run (three bases) = 0.1 out = 0.4 How many runs will the team score in an inning?

4.4 Events of Variable Length Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

4.4 Events of Variable Length 14 A manufacturer randomly puts one of six different prizes in a box of cereal. You bought 15 boxes but still didn’t get all 6 prizes Would you have valid complaint? “Cereal Complaint”

4.4 Events of Variable Length Name of Problem:. 2. Outcomes whose Random integer probabilities we know: correspondences: 3. RandInt(,, ) 4. ( Trials): 5. Answer: Vote

4.4 Events of Variable Length 16 End of 4.4

4.4 Events of Variable Length 17 “Cereal Prizes” - What's the best choice? 1. RandInt(1, 4, 1) 2. RandInt(1, 5, 1) 3. RandInt(1, 9, 1) 4. RandInt(1, 10, 1) 5. None of the above

4.4 Events of Variable Length 18 0 Points = Miss=.4 = 40% 1 Point = Make and miss =.6*.4 = 24% 2 Points = Make and make=.6*.6 = 36% Morgan is most likely to score 0 points! Counter-Intuitive!

4.4 Events of Variable Length 19 “1-1 Free Throw” What's the best choice? 1. RandInt(1, 6, 2) 2. RandInt(1, 10, 1) 3. RandInt(1, 10, 2) 4. RandInt(1, 40, 2)

4.4 Events of Variable Length 20 World’s worst animation coming up

4.4 Events of Variable Length 21

4.4 Events of Variable Length 22 Improved?

4.4 Events of Variable Length 23

4.4 Events of Variable Length 24 Watch out Pixar

4.4 Events of Variable Length

4.4 Events of Variable Length 26 “Grasshopper” - What's the best choice? 1. RandInt(1, 2, 1) 2. RandInt(1, 3, 1) 3. RandInt(1, 4, 1)

4.4 Events of Variable Length 27 “Scratch-off Ticket” What's the best choice? 1. RandInt(1, 10, 1) 2. RandInt(1, 20, 1) 3. RandInt(1, 30, 1) 4. RandInt(1, 40, 1) 5. RandInt(1, 100, 1) 6. RandInt(1, 500, 1)

4.4 Events of Variable Length 28 “Baseball Division Series” What's the best choice? 1. RandInt(1, 3, 1) 2. RandInt(1, 3, 3) 3. RandInt(1, 45, 3) 4. RandInt(1, 55, 3) 5. RandInt(1, 100, 1) 6. RandInt(1, 100, 5)

4.4 Events of Variable Length 29 “Baseball” - What's the best choice? More than 4

4.4 Events of Variable Length 30 “Cereal Complaint” - What's the best choice? 1.Yes 2.No 3.Can’t tell

4.4 Events of Variable Length 31 Meta - Material