Chapter - Performance Task (continued) A New Dartboard You are a graphic artist working for a company on a new design for the board in the , game of darts. You are eager to begin the project, but the team'annot decide on the terms of the game. Everyone agrees that the board should have four colors. But some want the probabilities of hitting each color to be equal, while others want them to be different. You offer to design two boards, one for each group. How do you get started? How creative can you be with your designs? 1. What 4 colors will you use for your board? Will it have a theme or a specic name? 2. How will you make sure that all four colors on one board have the same theoretical probability of being hit and that the colors on the other board do not have"! the same probability of being hit? 3. How will you choose the shape of your boards? What is important about the shape? Does the board with equal color probabilities have to be symmetrical? Does the board with unequal color probabilities have to be non-symmetrical? Explain. 4. How many sections will you have on each board? What is the minimum number of sections? How will you shape the sections of your boards? Do the sections on the board with equal probability need to be the same shape? Why or why not? 5. How will players score points using your board? Will \"each section be worth the same amount of points? 4 6. Calculate the probabilities of hitting each color on your board. Use mathematics to show that each color on one board has an equal probability of being hit and that colors on the other board do not have an equal probability of being hit