\\ Q Part 2: Matching Colors Matctho-Match April and June invented a two -player spinner game called Match/No-Match. A player spins this spinner twice on his or her turn. 0 If both spins land on the same color (a match), Player A scores. 0 If the two spins land on different colors (a no-match), player B scores. Since there are two matching combinations blue/blue and yellow/yellowthey decided that Player A should score only 1 point for a match and Player B should score 2 points for a Ito-match. Using the score sheet on the next page and a paper clips spinner, play the Match/No-Match game with a partner or by yourself. For each turn, record the color pair and award points to the appropriate player. 40 Match/No-Match Yellow Blue Turn Player Player Turn Player number Result A's score Player B's score number Result A's score B's score NM 2 13 M 2 M - 14 M 15 NM 4 2. NM 21 16 NM 2 5 M 17 NM M 2 a 18 NVM 2 NM 2 ' 19 - 8 NM M 2 20 m 9 m 21 10 NM 2 22 11 M 1 NM 23 M 12 NM 2 24 M 411. Use the results you collected to find the experimental probabilities of a match and a n match. The experimental probability is a probability that is determined through experimentation. (hint: remember that a fraction is just a division problem!) P(match) = number of turns that are matches = 2 = 50 % total number of turns 24 P(NO-match) = number of turns that are no matches = % total number of turns 24 2. List all the possible outcomes of a turn (two spins). Write the outcomes as pairs below like this: color on first spin/color on second spin, such as blue/blue. BLUE / BLUE 3. Use your list to determine the theoretical probabilities of a match and a no-match. Since all the outcomes are equally likely, the theoretical probability is... P(match) = number of outcomes that are matches = 2 - = 50% total number of possible outcomes 4 P(NO-match) = number of outcomes that are no-matches = SO % total number of possible outcomes 4. How do your results from parts 1 and 3 compare? SAME 5. Is Match/No - Match a fair game? If you think the game is fair, explain why. If you think it is not fair, explain how the rules could be changed to make it fair. " There is No balance . In the pornits 426. In 100 turns of the Matctho-Match game, how many times would you expect each of the following to occur? n f a. Two yellows 2A '0 r F\" b. Two blues 17 C six\" c. One yellow m one blue C; .r 4/ d (1. At least one yellow :2 Q g. e. A blue pr a yellow (did hf; 7. Look at your results from your actual game sheet. If you had stopped after ONE turn, what would have been the experimental probability of a match? If you had stopped after TWO turns, what would have been the experimental probability of a match? If you had stopped after THREE turns, what would have been the experimental probability of a match? Continue to nd the experimental probabilities based on your actual data through 24 turns and record your results in the table below. Experimental probability of a match (as a fraction) Experimental probability of a match (as a percent) Experimental probability of g match (as a decimal) 43 Experimental probability of a m (as a percent) Experimental probability of a match (as a decimal) Experimental probability of a match (as a fraction) 8. Using your decimal column, plot your data from #7 on the coordinate gd below. 1.0 :19 as 0.1 0.6 0.5 0.4 0.3 Probability of a Match 0.2 0-1 Wt- o.o ' Turn number