Assignment Alicia conducted an experiment with a pair of six-sided dice. With each roll, she added the value of the dice. Her results are shown below: How many trials did Alicia perform? How do you know? b Determine the experimental probability of rolling a 9. Answer as a fraction in lowest terms. C) Determine the experimental probability of rolling a 7. Answer as a fraction in lowest terms. d) Why are the experimental probability results in parts b and c surprising? e What could Alicia do in order to improve the results of her experiment i.e., reduce the number of "surprises"? 2. A bag contains an unknown number of marbles of various colours, one of which is blue. Cassy wants to determine the probability of selecting a blue marble from the bag at random. Cassy figures she has two choices: Count all the marbles, taking care to note how many are blue. This would provide the information necessary to calculate the theoretical probability of selecting a blue marble. 2) Conduct a number of trials of an experiment where a marble is removed at random, its colour noted and then put back in the bag. This would provide the data necessary to calculate the experimental probability of selecting a blue marble. Describe the advantages and disadvantages of each method. If you feel that either method is preferable, then state your preference with reasons for your choice. 3. Explain why are you more likely to have an experimental probability close to 50% if you flip a coin 5000 times than if you flip it only 50 times.Carter flipped a coin 1000 times and calculated an experimental probability of 48.8%. Allanah flipped a coin twice and got an experimental probability of 50%. She concluded that her results are "better." Is Allanah correct? Explain 5. Suppose you are using the random number generator on a TI-83 calculator. Identify the keying sequence you would follow to generate sets of 5 numbers representing the possible outcomes of two dice being rolled and their values added. 6 A donut shop carries six different kinds of jelly-filled donuts, including their famous "pineapple-filled" flavour. When Clarice ordered a mixed dozen of the jelly-filled donuts, the server put two of each kind into the box. On her way home, Clarice ran into Patrick and offered him a donut. Patrick picked one from the box and informed Clarice that he hoped it was not pineapple-filled since he was allergic to pineapple. What is the theoretical probability that Patrick's donut is pineapple-filled? b) If you were to simulate this situation with an experiment, you would not need twelve items but could conduct the experiment with only six items. Explain why this is true. c) Use a six-sided die, a graphing calculator, or a spreadsheet to collect data that you could use calculate the experimental probability of Patrick selecting a pineapple-filled donut from the box at random. Compare your final result with the theoretical probability. Conduct as many trials as you feel are necessary to provide a reasonable value for the experimental probability."Include any charts or tables that you use to record and/or organize the data