Question

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.

A-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.

B-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 w

Answer 1

The fairness of Ebony's random drawing method can be assessed by calculating the probability of drawing two gold or two silver chips for Betty and the probability of drawing one gold and one silver chip for Dawnie.

Step-by-step explanation:

The fairness of Ebony's method for determining the winner of the hat design contest can be evaluated by calculating the probability of each possible outcome. There are two scenarios for Betty to win: drawing two gold chips or two silver chips. For Dawnie to win, a gold and a silver chip must be drawn. To find the probabilities, we need to consider the total number of possible outcomes for drawing two chips without replacement.

Calculating Probabilities

For Betty to win (same color chips), the probability of drawing two gold is:

The combined probability for this scenario is (10/20) * (9/19). Similarly, the probability of drawing two silver chips is (10/20) * (9/19).

For Dawnie to win (different color chips), we have two scenarios:

The combined probability for Dawnie to win is the sum of these two scenarios.

After calculating these probabilities, we can determine if the contest is fair by seeing if each designer has an equal chance of winning.

Answer 2

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 two different colors will be pulled out is higher than that of the same color.