Class Activity 16M Using Fraction Multiplication and Addition to Calculate a Probability paper clip, an opaque bag, and blue, red, and green tiles would be helpful A game consists of spinning the spinner in Chess Activity 161, and then picking a small tile from a bag containing I bluetie, 3 red tiles, and I gruentile (All tiles are identical except for color, and the person picking a tile cannot see into the baj, so the choice of a tile is random.) To win the game, a contestant must pick the same color tile that the spinner landed on. So a contestant wins from either a blue wpin fol- lowed by a blue tile or a red spin followed by a red tile. 1. Make a guess What do you think the probability of winning the game is? 2. If the materials are available, play the game a number of times. Record the number of times you play the game each game consists of both a spin and a pick from the bags, and record the number of times you win. What fraction of the time did you win? How does this compare with your gues in part 1 3. To calculate the theoretical) probability of winning the game, imagine playing the game many times. Answer the questions below in order to determine the probability of winning the game. a. In the ideal, what fraction of the time should the spin be blue? Show this by shading the rectangle below In the ideal, what traction of those times when the spin is blue should the tile that is chosen be blue? Show this by further shading the rectangle below. Therefore, in the ideal, what fraction of the time is the spin blue and the tile blue Explain how you can determine this fraction from the shading of the rectangle and from the meaning of fraction multiplication b. In the ideal, what fraction of the time should the spin be red? Show this by shad- ing the rectangle below. In the ideal, what fraction of those times when the spin is rod should the tile that is chosen be red? Show this by further shading the rectangle below. Therefore, in the ideal, what fraction of the time is the spin red and the tile red? Explain how you can determine this fraction from the shading of the rectangle and from the meaning of fraction multiplication. c. In the ideal, what fraction of the time should you win the game, and therefore, what is the probability of winning the game? Explain why you can calculate this answer by multiplying and adding fractions. Compare your answer with parts 1 and 2. A rectangle representing playing the game many times