Open Middle®
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
How can you have a different number of red marbles but the same likelihood of selecting a red marble and both bags?
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
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
Another possible correct answer is:
Bag A: 1 red and 2 blue; Bag B: 3 red and 6 green
Another possible correct answer is:
Bag A: 3 red and 6 blue; Bag B: 2 red and 4 green
One possible answer is bag a would equal 2 red And 4 blue, bag b would equal 3 red and 6 green
Another possible correct answer is:
Bag A: 3 red and 6 blue; Bag B: 2 red and 4 green
Another possible correct answer is:
Bag A: 3 red and 6 blue and Bag B can equal 2 red and 4 green.
my teacher says that was wrong
Bag A: 1 red and 3 blue; Bag B: 2 red and 6 green
BagA 2 red and 4 blue BagB 3 red and 6 green
Bag A : 3 red and 6 blue
Bag B : 2 red and 4 green
Bag A : 3 Red and 6 Blue
Bag B : 2 Red and 4 Blue
Bag A: 3 red and 6 Blue
Bag B: 2 red and 4 blue
One answer is Bag 1. 3 red 6 blue
Bag 2. 2 red and 4 green
One answer is Bag 1. 3 red 6 blue
Bag 2. 5 red and 10 green
One answer is Bag 1. 1 red 2 blue
Bag 2. 5 red and 10 green
Bag A: 1 red and 3 blue
Bag B: 2 red and 6 blue.
Bag A: 1 red and 3 blue Bag B: 2 red and 6 blue
2 red and 4 blue for Bag 1 as for Bag 2 there is 3 red and 6 blue.
bag A,1 red 3 blue
bag B,2 red 6 blue
Bag A: 2 red and 4 blue; Bag B: 3 red and 6 green.
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.
Bag A: 2 red 4 blue
Bag B: 3 red 6 blue
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.
Bag1: 3 red, 2blue
Bag2: 5 red, 10 blue
1 red 3 blue
2 red 6 green
Bag A: 2 red, 4 blue
Bag B: 3 red, 6 blue
One answer is bag A is 3 red and 6 blue and bag B is 4 red and 8 green.
Bag A: 2 red 4 blue. ; 3 red 6 blue
Bag A: 2 red and 4 blue; Bag B: 3 red and 6 green
Bag A: 1 red and 4 blue; Bag B: 2 red and 8 green
2 red, 3 blue:6 red, 9 blue
Bag a: 3 red and 6 blue, Bag b: 4 red and 8 green
Bag A 2 red 4 blue; Bag B 3 red 6 green
Sebastian Sanchez
Bag A: 1 red 4 blue
Bag B: 2 red 8 green
Bag A : 3 red and 6 blue
Bag B : 4 red and 8 green
Bag A has 1 red and two blue.
Bag B has 4 red and 8 green.
Bag A has 1 red and 3 blue
Bag B has 2 red and 6 green
bag A has 1 red and 3 blue
bag B has 3 red and 9 green
bag A has 3 red and 9 blue
bag B has 9 red and 27 green
2 red marbles and 3 blue marbles in bag a and 6 red marbles and 9 blue marbles in bag b
one possible answer is bag a: 2 red and 6 blue; bag b: 5 red and 1 green
bag a: 3 red 6 blue bag b: 2 red 4 blue
Bag A: 3 red and 6 blue and Bag B can equal 2 red and 4 green.
bag a: 3 red and 6 blue and bag B equal 2 red and 4 green
Bag A : 3 Red and 6 Blue
Bag B : 2 Red and 4 Blue
Bag A: 3 red and 6 blue Bag B: 4 red and 8 blue.
Bag A: 3 red and 6 blue
Bag B: 4 red and 8 blue
Bag A: 3 red 6 blue
Bag b: 2 red 4 blue
Bag A: 2 red 6 blue
Bag B: 4 red 12 green
Bag A: 1 red 2 blue
Bag B: 4 red 8 green
Bag A: 2 red and 4 blue; Bag B: 3 red and 6 green
Bag Ahas 2 red and 4 blue while Bag B has 3 red and 6 green
Bag A has 2 red and 4 blue while Bag B has 3 red and 6 green
BagA:1 red and 2 blue BagB:3 red and 6 green
bA: 3 red, 9 blue. bB: 7 red, 21 green
A bag : 1 Red , 1 Bleu
B bag : 1 red, 1 Bleu
The red is 1/2 & 1/2 chance in both bags.
Bag A = 2 red, 3 blue
Bag B = 4 red, 6 blue
there is a 2/5 chance for each bag