Section 4.4

Events of

LengthVariable

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 Points2. 1 Point3. 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 $200 20 say $10030 say $5040 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

11

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

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 makessingle (one base) = 0.3 double (two bases) = 0.2home run (three bases) = 0.1 out = 0.4

How many runs will the team score in an inning?

4.4 Events of Variable Length

13

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

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

15

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

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?

Ran

dInt(1

, 6, .

..

Ran

dInt(1

, 10,

...

Ran

dInt(1

, 10,

...

Ran

dInt(1

, 40,

...

25% 25%25%25%

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

25

1 20-1

-2

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?

Ran

dInt(1

, 3, .

..

Ran

dInt(1

, 3, .

..

Ran

dInt(1

, 45,

...

Ran

dInt(1

, 55,

...

Ran

dInt(1

, 100

...

Ran

dInt(1

, 100

...

17% 17% 17%17%17%17%

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?

1. 0-1

2. 1-2

3. 2-3

4. 3-4

5. 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

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