Statistics and Probability
Question 1: Assume that a fair six-sided die is rolled three times.(a) What is the probability that the three numbers rolled sum to 18?(b) What is the probability that the three numbers rolled are all the same?(c) What is the probability that the three numbers rolled are all distinct?(d) What does it mean for two rolls of the die to be independent? Is it reasonable to assume that they are indeed independent? Explain your reasoning.Assume now that you are given the opportunity to play a game where you win £10 if you roll three 6, you win £5 if the numbers are all the same (different from 6), and you lose £1 otherwise.(e) What are the expected value and variance of your winnings? (f) You now play the game with a die that is not fair and shows the six different numbers with the probabilities: P(1) = 0.3, P(2) = 0.1, P(3) = 0.1, P(4) = 0.1, P(5) = 0.1, P(6) = 0. What is the expected value of your winnings?
Our experts will write you a top-quality paper and revise it an unlimited number of times until you're 100% satisfied - or offer a refund.