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Mathematical Practices, Mathematics for Teachers: Activities, Models, and Real-Life Examples 1st Edition

Mathematical Practices, Mathematics for Teachers: Activities, Models, and Real-Life Examples (1st Edition)

Book Edition1st Edition
Author(s)Larson
ISBN9781285447100
PublisherCengage
SubjectMath
Chapter 16, Start of Chapter, Activity, Exercise 1
Page 614

Put 2 green marbles and 1 blue marble in a bag. Perform each experiment 36 times. Record each result as GG (green, green), GB (green, blue), or BB (blue, blue) using tally marks. A result of GB or BG represents the same result.

 

Randomly draw two marbles from the bag.

Explanation

If you have 2 green balls and 1 blue ball, the probability of getting a green ball is 2/3, and the probability of getting a blue ball is 1/3.
Since it was stated that a combination of BB is possible, then I suppose the first ball drawn will be put back inside the bag.

So the probability of getting a green ball the second time, having a combination of GG (green,green) is 2/3*2/3 = 4/9

The probability of getting a blue ball the second time, having a combination of BB (blue,blue) is 1/3*1/3 = 1/9

The probability of getting a blue ball the second time while having green as the first one, having a combination of GB (green,blue) is 2/3*1/3= 2/9

The probability of getting a green ball the second time while having blue as the first one, having a combination of BG (blue,green) is 1/3*2/3= 2/9

Since the results GB and BG was stated to be the same, then the probability of getting both combination is 2/9 + 2/9 = 4/9

Multiplying these probability values by 36, we get:

GG: 4/9 * 36 =16
BB: 1/9 * 36 =4
GB&BG:4/9 * 36 =16

 

Drawing these as tally marks (I also included BB in the table below):

GG(IIIII) (IIIII) (IIIII) I
GB(IIIII) (IIIII) (IIIII) I
BBIIII

Answer

The answer would be:

GG(IIIII) (IIIII) (IIIII) I
GB(IIIII) (IIIII) (IIIII) I
BBIIII

 

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