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Probability with Marbles

Directions: There are _____ red marbles and _____ blue marbles in Bag A. There are _____ red marbles and _____ green marbles in Bag B.

Using the digits 1 to 9 at most one time each, fill in the boxes to make the probability of drawing a red marble from either bag the same.

Extension: Change the problem such that the number of green marbles is a two digit number.

Hint

Hint

How can you have a different number of red marbles but the same likelihood of selecting a red marble and both bags?

Answer

Answer

There are several correct answers:
Bag A: 2 red and 4 blue; Bag B: 3 red and 6 green
Bag A: 3 red and 6 blue; Bag B: 4 red and 8 green
Bag A: 1 red and 2 blue; Bag B: 4 red and 8 green
Bag A: 1 red and 3 blue; Bag B: 2 red and 6 green
Bag A: 1 red and 4 blue; Bag B: 2 red and 8 green

Source: Erick Lee

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56 comments

  1. Bibiana Rodriguez

    Another possible correct answer is:

    Bag A: 1 red and 2 blue; Bag B: 3 red and 6 green

  2. Bibiana Rodriguez

    Another possible correct answer is:
    Bag A: 3 red and 6 blue; Bag B: 2 red and 4 green

  3. One possible answer is bag a would equal 2 red And 4 blue, bag b would equal 3 red and 6 green

  4. Another possible correct answer is:
    Bag A: 3 red and 6 blue; Bag B: 2 red and 4 green

  5. Another possible correct answer is:

    Bag A: 3 red and 6 blue and Bag B can equal 2 red and 4 green.

  6. Bag A: 1 red and 3 blue; Bag B: 2 red and 6 green

  7. Bag A : 3 red and 6 blue
    Bag B : 2 red and 4 green

  8. Bag A : 3 Red and 6 Blue
    Bag B : 2 Red and 4 Blue

  9. Bag A: 3 red and 6 Blue
    Bag B: 2 red and 4 blue

  10. Terrence Phillips

    One answer is Bag 1. 3 red 6 blue
    Bag 2. 2 red and 4 green

  11. Terrence Phillips

    One answer is Bag 1. 3 red 6 blue
    Bag 2. 5 red and 10 green

  12. Terrence Phillips

    One answer is Bag 1. 1 red 2 blue
    Bag 2. 5 red and 10 green

  13. Bag A: 1 red and 3 blue
    Bag B: 2 red and 6 blue.

  14. Bag A: 1 red and 3 blue Bag B: 2 red and 6 blue

  15. 2 red and 4 blue for Bag 1 as for Bag 2 there is 3 red and 6 blue.

  16. bag A,1 red 3 blue
    bag B,2 red 6 blue

  17. Bag A: 2 red and 4 blue; Bag B: 3 red and 6 green.

  18. Trinity Maguadog

    You can do 1 red and 2 blue for bag A, and 3 red and 6 green for bad B. Another way is to have 1 red and 2 blue for bag A, and 6 red and 12 green for bad B.

  19. Cristian Alvarado

    Bag A: 2 red 4 blue
    Bag B: 3 red 6 blue

  20. May I recommend that it be added to this problem that students provide the probability for drawing red from each bag? The reason I suggest that is because I have noticed a misconception students have when solving this. Consider the solution provided by Cristian Alvaredo. Bag A: 2 red 4 blue and Bag B: 3 red 6 blue is a correct solution. But without asking for the probability of drawing a red, we might not catch the misconception. Some students will say that the probability is 1/2 for both bags instead of 1/3.

  21. Bag1: 3 red, 2blue
    Bag2: 5 red, 10 blue

  22. 1 red 3 blue
    2 red 6 green

  23. Bag A: 2 red, 4 blue

    Bag B: 3 red, 6 blue

  24. One answer is bag A is 3 red and 6 blue and bag B is 4 red and 8 green.

  25. Bag A: 2 red 4 blue. ; 3 red 6 blue

  26. Bag A: 2 red and 4 blue; Bag B: 3 red and 6 green

  27. Bag A: 1 red and 4 blue; Bag B: 2 red and 8 green

  28. 2 red, 3 blue:6 red, 9 blue

  29. Bag a: 3 red and 6 blue, Bag b: 4 red and 8 green

  30. Sebastian Sanchez

    Bag A 2 red 4 blue; Bag B 3 red 6 green

    Sebastian Sanchez

  31. Bag A: 1 red 4 blue

    Bag B: 2 red 8 green

  32. Bag A : 3 red and 6 blue
    Bag B : 4 red and 8 green

  33. Bag A has 1 red and two blue.
    Bag B has 4 red and 8 green.

  34. Bag A has 1 red and 3 blue
    Bag B has 2 red and 6 green

  35. bag A has 1 red and 3 blue
    bag B has 3 red and 9 green

  36. bag A has 3 red and 9 blue
    bag B has 9 red and 27 green

  37. 2 red marbles and 3 blue marbles in bag a and 6 red marbles and 9 blue marbles in bag b

  38. one possible answer is bag a: 2 red and 6 blue; bag b: 5 red and 1 green

  39. bag a: 3 red 6 blue bag b: 2 red 4 blue

  40. Bag A: 3 red and 6 blue and Bag B can equal 2 red and 4 green.

  41. bag a: 3 red and 6 blue and bag B equal 2 red and 4 green

  42. Bag A : 3 Red and 6 Blue
    Bag B : 2 Red and 4 Blue

  43. Bag A: 3 red and 6 blue Bag B: 4 red and 8 blue.

  44. Bag A: 3 red and 6 blue
    Bag B: 4 red and 8 blue

  45. Bag A: 3 red 6 blue
    Bag b: 2 red 4 blue

  46. Bag A: 2 red 6 blue
    Bag B: 4 red 12 green

  47. Bag A: 1 red 2 blue
    Bag B: 4 red 8 green

  48. Bag A: 2 red and 4 blue; Bag B: 3 red and 6 green

  49. Bag Ahas 2 red and 4 blue while Bag B has 3 red and 6 green

  50. Bag A has 2 red and 4 blue while Bag B has 3 red and 6 green

  51. briana broussard

    BagA:1 red and 2 blue BagB:3 red and 6 green

  52. bA: 3 red, 9 blue. bB: 7 red, 21 green

  53. A bag : 1 Red , 1 Bleu
    B bag : 1 red, 1 Bleu

    The red is 1/2 & 1/2 chance in both bags.

  54. Bag A = 2 red, 3 blue
    Bag B = 4 red, 6 blue
    there is a 2/5 chance for each bag

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