In: Statistics and Probability
a) When all factors are taken into account, an insurance company estimates that the probability of my father making a claim for damages to his pontoon boat for $5000 is 0.1, and that the probability of the pontoon boat being totally destroyed is .005. Should that tragedy happen, the company will have to pay $15,000. The company charges my father $1000 for the insurance policy. What is the expected value of this policy to my father?
b) The world famous gambler and statistics professor from Columbus, Michelle Duda, proposes the following game of chance. You roll a fair die. If you roll a 1, then Michelle pays you $25. If you roll a 2, Michelle pays you $5. If you roll a 3, you win nothing. If you roll a 4 or a 5, you must pay Michelle $10, and if you roll a 6, you must pay Michelle $15. What is the expected value of Michelle's game?