The following grid consists of five rows and nine columns. You are to place a penny on the square marked START. Roll a d
Posted: Mon Jul 11, 2022 11:57 am
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 row andleft one square. If the roll is odd, move down one row andright one square. One game consists of four rolls of the die. At the end of the game your penny will be in one of thesquares on the bottom row. You are to play the game 16 times. Place a tally mark on the square in the bottom row positionafter 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.
1A) The model used in this game is called the binomialdistribution. List the characteristics of the binomial distributionin the space below.
1B) Use the binomial distribution to find the probabilityof ending on each of the five possible final positions of the abovegame board. Use the binomialpdf function on the TI to do yourwork. Number the final positions 1, 2, 3, 4, 5 from left to righton the bottom row, and give the probability of ending in thatposition. Some tips to get you started. Think of rolling an even as asuccess and rolling an odd as a failure. How many successes do youneed to get to Position 1, how many successes do you need to get toPosition 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 =
1C) Compare the results of your games to the results usingthe probability as computed above. List your observations inthe space provided.
Now play the game again with the following changes in the movementrule. Roll a die and move down one row and left one space if theroll is 1 or 2, or move down one row and right one space if theroll is 3, 4, 5, or 6. Record your results below. Position 1:Position 2: Position 3:Position 4:Position 5:
1D) How are the two games different?
1E) How are the two games similar?
1A) The model used in this game is called the binomialdistribution. List the characteristics of the binomial distributionin the space below.
1B) Use the binomial distribution to find the probabilityof ending on each of the five possible final positions of the abovegame board. Use the binomialpdf function on the TI to do yourwork. Number the final positions 1, 2, 3, 4, 5 from left to righton the bottom row, and give the probability of ending in thatposition. Some tips to get you started. Think of rolling an even as asuccess and rolling an odd as a failure. How many successes do youneed to get to Position 1, how many successes do you need to get toPosition 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 =
1C) Compare the results of your games to the results usingthe probability as computed above. List your observations inthe space provided.
Now play the game again with the following changes in the movementrule. Roll a die and move down one row and left one space if theroll is 1 or 2, or move down one row and right one space if theroll is 3, 4, 5, or 6. Record your results below. Position 1:Position 2: Position 3:Position 4:Position 5:
1D) How are the two games different?
1E) How are the two games similar?