Marble Game
This problem gives you the chance to:
• use probability in an everyday situation
Bag A Bag B
Linda has designed a marble game.
1. Bag A contains 3 marbles –
one red, one blue and one green. R
G R
Bag B contains 2 marbles – B B
one red and one blue.
To play this game, a player draws one marble from each bag without looking.
If the two marbles match (are the same color), the player wins a prize.
What is the theoretical probability of winning a prize at a single try? _____________
Show your work.
Win No Win
2. Here are the results for the first 30 games. (Match) (No Match)
How do the results in this table and the theoretical
probability you found compare?
_______________________________________
Explain any differences.
______________________________________________________________________________
______________________________________________________________________________
Grade 8 Marble Game
Copyright © 2009 by Mathematics Assessment 44
Resource Service. All rights reserved.
,3. Linda has designed a second game.
The spinner has nine equal sections.
Red
Gold
To play the game, a player spins the spinner. Blue
If the spinner lands on a Gold section, Red
the player wins a prize.
Gold
Gold
Does the player have a better chance of winning with Red
the bag game or the spinner game? Gold
Red
__________________________________________
Explain your reasoning.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
7
Grade 8 Marble Game
Copyright © 2009 by Mathematics Assessment 45
Resource Service. All rights reserved.
, Marble Game Rubric
The core elements of performance required by this task are:
• listed here
section
Based on these, credit for specific aspects of performance should be assigned as follows points points
1. 2 1 1
Gives correct answer: =
6 3
Lists all possibilities: RR, RB, BR, BB, GR, GB 1
p(RR or BB) = 2/6 or 1/3 1
or !
or
1 1
Shows work such as: Probability R " R = # 1
3 2
1
1 1
Probability B " B = #
3 2
! 1 1
Probability both same color = +
6 6 3
!
2. These results are quite close; 1
!
but the number of trials is not large enough to give an accurate estimate. 1
or
Explains that from these results the experimental probability
9 3
= = = 0.3
30 10
The theoretical probability = 0.33 recurring 1
2
!
3. Gives correct answer: the spinner game 1
Shows work such as: 1
the probability of winning on the spinner game is 4/9 = 0.44 recurring
2
Total Points 7
Grade 8 46
Copyright © 2009 by Mathematics Assessment
Resource Service. All rights reserved.
This problem gives you the chance to:
• use probability in an everyday situation
Bag A Bag B
Linda has designed a marble game.
1. Bag A contains 3 marbles –
one red, one blue and one green. R
G R
Bag B contains 2 marbles – B B
one red and one blue.
To play this game, a player draws one marble from each bag without looking.
If the two marbles match (are the same color), the player wins a prize.
What is the theoretical probability of winning a prize at a single try? _____________
Show your work.
Win No Win
2. Here are the results for the first 30 games. (Match) (No Match)
How do the results in this table and the theoretical
probability you found compare?
_______________________________________
Explain any differences.
______________________________________________________________________________
______________________________________________________________________________
Grade 8 Marble Game
Copyright © 2009 by Mathematics Assessment 44
Resource Service. All rights reserved.
,3. Linda has designed a second game.
The spinner has nine equal sections.
Red
Gold
To play the game, a player spins the spinner. Blue
If the spinner lands on a Gold section, Red
the player wins a prize.
Gold
Gold
Does the player have a better chance of winning with Red
the bag game or the spinner game? Gold
Red
__________________________________________
Explain your reasoning.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
7
Grade 8 Marble Game
Copyright © 2009 by Mathematics Assessment 45
Resource Service. All rights reserved.
, Marble Game Rubric
The core elements of performance required by this task are:
• listed here
section
Based on these, credit for specific aspects of performance should be assigned as follows points points
1. 2 1 1
Gives correct answer: =
6 3
Lists all possibilities: RR, RB, BR, BB, GR, GB 1
p(RR or BB) = 2/6 or 1/3 1
or !
or
1 1
Shows work such as: Probability R " R = # 1
3 2
1
1 1
Probability B " B = #
3 2
! 1 1
Probability both same color = +
6 6 3
!
2. These results are quite close; 1
!
but the number of trials is not large enough to give an accurate estimate. 1
or
Explains that from these results the experimental probability
9 3
= = = 0.3
30 10
The theoretical probability = 0.33 recurring 1
2
!
3. Gives correct answer: the spinner game 1
Shows work such as: 1
the probability of winning on the spinner game is 4/9 = 0.44 recurring
2
Total Points 7
Grade 8 46
Copyright © 2009 by Mathematics Assessment
Resource Service. All rights reserved.
