The following grid consists of five rows and nine columns. You are to place a penny on the square marked START. Roll a d

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The following grid consists of five rows and nine columns. Youare to place a penny on the square marked START. Roll a die. If you roll an even number you will move down one rowand left one square. If the roll is odd, move down onerow and right one square. One game consists of four rolls ofthe die. At the end of the game your penny willbe in one of the squares on the bottom row. You are toplay the game 16 times. Place a tally mark on the square inthe bottom row position after each game.
But wait! Before you begin playing, you are to predict the finaloutcome of the 16 games by placing numbers in the bottom row thatyou anticipate as your final result. Yes, the sum of your guessesin the bottom row is 16.
If you don’t have a die use an app, like Dice Roll, to simulaterolling a die.
START
1. So, how did you do with your predictions? Were yousurprised at your results? Discuss symmetry and the cell locationsthat are impossible.
2. The model used in this game is called the binomialdistribution. List the characteristics of the binomialdistribution in the space below.
3. Use the binomial distribution to find theprobability of ending on each of the five possible final positionsof the above game board. Usethe binomialpdf function on the TI to do your work.Number the final positions 1, 2, 3, 4, 5 from left to right on thebottom row, and give the probability of ending in thatposition.
Some tips to get you started. Think of rolling an even asa success and rolling an odd as a failure. How many successes doyou need to get to Position 1, how many successes do you need toget 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 theresults using the probability as computed above. Listyour observations in the space provided.
Now play the game again with the followingchanges in the movement rule. Roll a die and move down one row andleft one space if the roll is 1 or 2, or move down one row andright one space if the roll is 3, 4, 5, or 6. Record yourresults below.
Position 1:
Position 2:
Position 3:
Position 4:
Position 5:
5. How are the two games different?
6. How are the two games similar?