Homework for Day 1 Design and carry out a simulation to answer the following questions. (1) A couple has high hopes of having a "gentleman's family." This usually means it would have two children, the first being a son and second a daughter. Assuming the probabilities of having a boy or girl are equally likely for each birth, how likely is it the couple will end up with its dream family? (2) A computer game awards a special shield to the player 20% of the time after the player completes a level of the game. David plans to begin studying for a test once he obtains the special shield. It takes him roughly 15 minutes to complete a level. Estimate how long you believe it will be before David begins his studying. (3) A very large company must make budget cuts to remain in business. The chief executive officer plans to form a committee including five randomly selected employees. 50% of the employees are fiscally conservative, 30% liberat, and 20% moderate. The hope is that at least one of each group (conservative, liberal, moderate) is chosen for the commitree so employees feel represented and no one group has the majority. The names of all employees are printed on labels and five are drawn. Does this appear to be a suitable method to achieve a committee the employees will deem fair? 2) Adult rattlesnakes tend to hide rather than bite humans. Silly creatures that they are, humans ofte go in search of rattlesnakes. Bite records seem to show that rattlesnakes are aware that humans a too big to eat. Medical records of rattlesnake bites show that about 30% of the bites contain no venom. These are known as dry bites. Note: Consider rattlesnake bites independent events. (a) What is the probability that two rattlesnake victims get dry bites? (b) If you are bitten by a rattlesnake, what is the probability the bite contains venom? (c) If an emergency center in West Texas sees six patients with rattlesnake bites during the fall rattlesnake round-up, what is the probability the first five bites contain venom and the last one do not contain venom?.