Bonita and Deion are using the spinners from the Making Purple game in Problem 2.1. They take turns spinning. If the colors on the two spinners make purple, Dion scores. If they do not make purple, Bonita scores. For this to be a fair game, how many points should Deion score when the spinners make purple, and how many points should BOnita score when they do not make purple?
Jeg vet ikke.
To determine the number of points Deion should score when the spinners make purple, and the number of points Bonita should score when they do not make purple, we need to understand the concept of fairness in a game.
In a fair game, each player should have an equal chance of winning. In this case, if the spinners make purple, Deion scores, and if they do not make purple, Bonita scores. Therefore, to make the game fair, the average number of points Deion scores when the spinners make purple should be equal to the average number of points Bonita scores when they do not make purple.
Let's break down the problem further.
First, let's determine the number of possible outcomes for each spinner. If we assume that each spinner has six colors, the number of possible outcomes for each spinner is six.
To find the total number of outcomes for both spinners, we multiply the number of outcomes for each spinner. In this case, it would be 6 (from the first spinner) multiplied by 6 (from the second spinner), which equals 36 possible outcomes.
Next, let's determine the number of outcomes where the spinners make purple. If we assume that there is only one color on each spinner that makes purple when combined, then there is only one outcome where the spinners make purple.
Finally, to make the game fair, the average number of points Deion scores (when the spinners make purple) should be equal to the average number of points Bonita scores (when they do not make purple).
Since there is only one outcome where the spinners make purple out of 36 possible outcomes, Deion should score 1 out of the 36 points.
To find the average number of points Bonita scores when they do not make purple, we subtract the one outcome where the spinners make purple from the total number of possible outcomes: 36 - 1 = 35.
Therefore, Bonita should score 35 out of the 36 points when the spinners do not make purple.
In summary, to make the game fair, Deion should score 1 point when the spinners make purple, and Bonita should score 35 points when they do not make purple.