Question

Suppose you are given a six-sided die, that might be biased in an unknown way. Explain how to use die rolls to generate unbiased coin flips, and determine the expected number of die rolls until a coin flip is generated. Now suppose instead you want to generate unbiased die rolls (from a six-sided die) given your potentially biased die. Explain how to do this, and again determine the expected number of biased die rolls until an unbiased die roll is generated. For both problems, you need not give the most efficient solution – simple, non-recursive are all that we are looking for – however, your solution should be reasonable, and exceptional solutions will receive exceptional scores.

Is it possible to get detailed answer on this one?

Answer 1

let X be the number of die rolls untill we roll a specific number.let p be the probability that we roll the specific number and q=1-p be the probability that we roll any of the other numbers .we know,

E[X] = 1p+2pq+3pq²+4pq³+...................