(Solved): Part 1: The following grid consists of five rows and nine columns. You are to place a penny on ...

Part 1: The following grid consists of five rows and nine columns. You are to place a penny on the square marked START. Roll a die. If you roll an even number you will move down one row and left one square. If the roll is odd, move down one row and right one square. One game consists of four rolls of the die. At the end of the game your penny will be in one of the squares on the bottom row. You are to play the game 16 times. Place a tally mark on the square in the bottom row position after each game. But wait! Before you begin playing, you are to predict the final outcome of the 16 games by placing numbers in the bottom row that you anticipate as your final result. Yes, the sum of your guesses in the bottom row is 16. If you don't have a die use an app, like Dice Roll, to simulate rolling a die. 1. So, how did you do with your predictions? Were you surprised at your results? Discuss symmetry and the cell locations that are impossible. 2. The model used in this game is called the binomial distribution. List the characteristics of the binomial distribution in the space below. 3. Use the binomial distribution to find the probability of ending on each of the five possible final positions of the above game board. Use the bingmialedf function on the TI to do your work. Number the final positions 1, 2, 3, 4, 5 from left to right on the bottom row, and give the probability of ending in that position. Some tips to get you started. Think of rolling an even as a success and rolling an odd as a failure. How many successes do you need to get to Position 1 , how many successes do you need to get to Position 2 , and so on. Position 1: n?=?p=x=P= Position 2: n?=?p=x=P= Position 3: n?=p=x=P= Position 4: n?=?p=x=P= Position 5: n?=p=x=P= 4. Compare the results of your games to the results using the probability as computed above. List your observations in the space provided.