Question

A family math night at your school includes the following activity. A bag is filled with 10 small bears that are identical except that 3 are yellow and 7 blue. The directions for the game are as follows:

Win a prize if you guess the correct number of yellow bears in the bag! There are 10 bears in the bag. Some are yellow and the rest are blue. Here is what you do:

1. Reach into the bag, mix well, and pick out a bear.
2. Get a sticky note that is the same color as your bear and write your name and your guess on the note and add it to the other notes of the same color.
3. Put your bear back in the bag and mix well.

The sticky notes will be organized in columns of 10 so that they are easy to count.

A.         How will the students be able to use the results of this activity to estimate the number of yellow bears in the bag? (8 points)

B.         What do you expect to happen as more kids play this game? (4 points)

C.        What are at least 2 modifications you would make to this game if you were actually going to use this for your own math night? (8 points)

Answer 1

Solution

Part (A)

Estimate the number of yellow bears in the bag

= 10 x proportion of yellow sticky notes

= 10 x {(Number of yellow sticky notes)/ (Number of yellow sticky notes + (Number of blue sticky notes))   Answer

Part (B)

As more kids play this game, it is expected that the estimate of the number of yellow bears in the bag as obtained by the process outlined in Part (A) would get closer to the actual number of yellow bears in the bag. Answer [as sample size increases, sample proportion gets closer to the population proportion]

Part (C)

Modification 1:

Increase the number of bears in the bag to, say 200 in a known ratio of yellow to blue bears . Allow the participants to mix and pick 5 bears at random, return the bears to the bag and then guess the number of yellow bears in the bag. The number of yellow bears they got and their guess are along with the name of the participant are reported on a yellow sticky note and added to the other notes.    

Modification 2:

Further increase the number of bears in the bag to, say 500 in a known ratio of yellow to blue bears . Allow the participants to mix and pick 5 bears at random, not to return the bears to the bag and then to guess the number of yellow bears in the bag. The number of yellow bears they got and their guess are along with the name of the participant are reported on a yellow sticky note and added to the other notes.     

Answer

DONE