Question

Please help!

Ebony owns a number of shops. She keeps careful records about which products sell best and notes ideas about how to increase sales. One of Ebony’s stores is a small shop that sells hats and caps. Ebony held a contest for the best hat design, planning to award a camera to the designer with the winning entry. She received numerous entries and narrowed her choice for first place to two designs; however, she couldn’t decide between Dawnie’s design and Betty’s design. Since Ebony couldn’t decide which of these two designs was better, she decided to hold a random drawing to determine the winner. Ebony planned to randomly pull chips from a bag. She put 20 chips in the bag: 10 gold chips and 10 silver chips. Ebony says she will pull 2 chips out of the bag, one at a time. If the 2 chips are the same color, she will give the camera to Betty. If the 2 chips are different colors, she will give the camera to Dawnie. Is this method fair? If it is not, explain who has an advantage in the drawing and how great the advantage is. Show your work and explain your reasoning.

Answer 1

Answer: No. The method is not fair.

The probability of pulling a gold or a silver for the first time is 1/10. The probability of getting the same color the second time is 1/9. The probability of getting a different color on the second pullout is still 1/10. Therefore, the chance that same colors will be pulled out is higher than that of different colors. Betty has an advantage in the drawing by 1.1%.

Solution:

Probability of same color:

1/10+1/9

9/90+10/90

21.1%

Probability of different colors

1/10+1/10

2/10

20%

21.1%-20%=1.1%