Cereal Toys: A certain brand of cereal is running a promotion where you can get 1 toy in each box purchased. There are 5 different toys. I wish to collect one set of these toys to give as a gift. Assuming the toys are randomly distributed among the boxes, how many boxes should I expect to buy before I have all 5 toys? Perform a simulation and repeat it 20 times. What is the average number of boxes you needed to buy before a set was obtained? Dice Rolling: Italian gamblers used to bet on the total number of dots rolled on three regular six-sided dice. They believed the chance of rolling a nine ought to equal the chance of rolling a total of 10 since there were an equal number of different ways to get each sum. However, experience showed that these did not occur equally often. The gamblers asked Galileo for help with the apparent contradiction, and he resolved the paradox. Can you do the same? Please answer the question in a well-written paragraph or series of paragraphs. Be sure to explain both why the gamblers were confused and what the actual probabilities are. You may include evidence from actual trials, simulations, and theoretical calculations