In 12,000 independent tosses of a die, it landed on "1" 2,500 times. Is it reasonable to assume that the die is not fair?
(a) Let Y denote the number of times the die will land on "1" when tossed 12,000 times, assuming the die is far. What is the distribution of Y ? Why?
(b) Use Chebychev's inequality to calculate an upper bound on the chances that Y will deviate from it's expected value by more than 499?
(c) Now use your calculation from part (b) to answer the question.