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B85, 43b, Probability problems: Dice games for two players part 2 of 2 (Student view), Grade 6, April 29, 2004, raw footage [video]. Retrieved from https://doi.org/doi:10.7282/t3-feqd-sm07
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TitleB85, 43b, Probability problems: Dice games for two players part 2 of 2 (Student view), Grade 6, April 29, 2004, raw footage
PublisherNew Brunswick, N.J.: Robert B. Davis Institute for Learning, 2004-05-10, c2004-05-10
Persistent URLhttps://doi.org/doi:10.7282/t3-feqd-sm07
DescriptionThis video is a continuation of the first session that 6th grade students from the Plainfield, NJ district explored probability through dice games in an after-school enrichment program. In this video (video 43b, part 2 of 2) the second Dice game is introduced by Researcher Alice Alston. This video follows the students (Partners: Adanna & Justina; Chanel & Danielle; Shanae & Kianja) as they work on the following problem:
Dice game with two ordinary dice: Roll two dice. If their sum is 2, 3, 4, 10, 11 or 12, player A gets one point (and player B gets 0). If their sum is 5, 6, 7, 8, or 9, player B gets one point (and player A gets 0). Continue rolling the dice. The first person to get ten points is the winner. (1) Is this a fair game? Why or why not? (2) Play the game with a partner. Do the results of playing the game support your answer? Explain. (3) If you think the game is unfair, how could you change it so that it could be fair?
[Note: The game favors Player B with a ⅔ probability of winning a point and a probability of approximately .935 of winning a game.]
The video begins with Kianja explaining her reasoning for awarding 2 points to player B from the first Dice game with one ordinary dice (see video 43a, part 1 of 2) to make the game fair by weighting the outcomes so that the point system is equal between the players.
In the first dice game, the students claimed that it was an unfair game. Many of the students begin this activity with the claim that player A, with 6 sums (player B has 5 sums) is favored to win the game.
Chanel, like many others, claims that player A is favored, but she is convinced, after two experimental trials with B as the winner, that player A's presumed advantage is neutralized with two less likely sums of 11 and 12. Chanel and her partner Danielle do not investigate why 11 and 12 are difficult: they simply observe that these numbers are not rolled often. Other students followed in this video create a sample space with 21 outcomes and conclude that Player B has a better chance to win. Kianja emphasizes the relative probabilities: 13/21 to 8/21.
Justina and Adanna attend to the number of ways each sum can be obtained. To make the game fair, they do so by first making the total number of outcomes equal by omitting one outcome, and then assigning half of the outcomes to each player. They played the game using this rule and established that both Player A and B win the game equally, thus providing evidence for a fair game.
Dice game with two ordinary dice: Roll two dice. If their sum is 2, 3, 4, 10, 11 or 12, player A gets one point (and player B gets 0). If their sum is 5, 6, 7, 8, or 9, player B gets one point (and player A gets 0). Continue rolling the dice. The first person to get ten points is the winner. (1) Is this a fair game? Why or why not? (2) Play the game with a partner. Do the results of playing the game support your answer? Explain. (3) If you think the game is unfair, how could you change it so that it could be fair?
[Note: The game favors Player B with a ⅔ probability of winning a point and a probability of approximately .935 of winning a game.]
The video begins with Kianja explaining her reasoning for awarding 2 points to player B from the first Dice game with one ordinary dice (see video 43a, part 1 of 2) to make the game fair by weighting the outcomes so that the point system is equal between the players.
In the first dice game, the students claimed that it was an unfair game. Many of the students begin this activity with the claim that player A, with 6 sums (player B has 5 sums) is favored to win the game.
Chanel, like many others, claims that player A is favored, but she is convinced, after two experimental trials with B as the winner, that player A's presumed advantage is neutralized with two less likely sums of 11 and 12. Chanel and her partner Danielle do not investigate why 11 and 12 are difficult: they simply observe that these numbers are not rolled often. Other students followed in this video create a sample space with 21 outcomes and conclude that Player B has a better chance to win. Kianja emphasizes the relative probabilities: 13/21 to 8/21.
Justina and Adanna attend to the number of ways each sum can be obtained. To make the game fair, they do so by first making the total number of outcomes equal by omitting one outcome, and then assigning half of the outcomes to each player. They played the game using this rule and established that both Player A and B win the game equally, thus providing evidence for a fair game.
Math ToolWorksheet with problem statements, Fair dice
Math StrandProbability
Math ProblemDice games
NCTM Grade Range6-8
NCTM Content StandardData analysis and probability
NCTM Process StandardProblem solving, Communication
Forms of Reasoning, Strategies and HeuristicsGuessing and checking, Making conjectures
Grade Level6
Student ParticipantsKianja (student), Justina (student), Adanna (student), Sha' Nae (student), Shanei (student)
MediatorsMaher, Carolyn Alexander (Researcher), Powell, Arthur B. (Researcher), Alston, Alice (Researcher)
SettingInformal learning
Student GenderFemale
Student EthnicityBlack
Camera ViewsStudent view
Date Captured2004-05-10
Local IdentifierB85-20040429-PLHUB-SV-IML-GR6-PROB-DICE-RAW
Related Publication
Type: Related publication
Label: Ph.D dissertation references the video footage [TITLE OF VIDEO B??, ..]
Date: 2008
Author: Shay, Kathleen B. (Rutgers Graduate School of Education)
Name: TRACING MIDDLE SCHOOL STUDENTS' UNDERSTANDING OF PROBABILITY: A LONGITUDINAL STUDY
Reference: https://doi.org/doi:10.7282/T3BR8SGM
Type: Related publication
Label: Ph.D dissertation references the video footage [TITLE OF VIDEO B??, ..]
Date: 2008
Author: Shay, Kathleen B. (Rutgers Graduate School of Education)
Name: TRACING MIDDLE SCHOOL STUDENTS' UNDERSTANDING OF PROBABILITY: A LONGITUDINAL STUDY
Reference: https://doi.org/doi:10.7282/T3BR8SGM