5. [Iii points} Specify an appropriate box model for each of the following experiments. You should assume that you will draw tickets from the box with replacement and you should specify the box model in such a waI that the sum of the selected ticket values will equal the quantity to be calculated. A complete answer should identifj,r the following: the values of the tickets in the box, how man},r tickets have each value, and the number of draws from the box is}- {a} A single fair die is rolled 2W] times and the sum of the odd numbers {rolls of .l, 3, or 5:! is computed. Solution: There are six equally likely possible outcomes of a single roll, so we need six tickets in our box. we want the sum of the ticket values to include odd numbers but not even numbers, so our ticket values should be {1, D, 3, U, 5, D]. We will draw a = 20G times, with replacement. {b} a pair of fair dice is rolled IUD times. The number of times that a double [both dice produce the same number) is rolled is counted. Solution: This is a counting problem, so we require a [1-1 box. Each ticket should correspond to an outcome of rolling a pair of dice. There are 6 x 6 = 36 possible outcomes. Because the dice are fair, each outcome is equally likely, so 35 tickets will sufce. Those that correspond to doubles should be labelled I; the rem ainder should be labelled 0. There are 6 possible ways to roll a double, so we need 6 tickets labelled l and 31] tickets labelled D. {Equitalentlgn we could have 1 ticket labelled l and 5 tickets labelled 0.] We will draw n : 1130 times, with replacement