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