Please show all of your steps and explanations. Thanks!

3. Binomial From Nowhere (10 points) Consider repeatedly rolling a fair 6-sided die, each roll being independent of the others. Define the random variable Y to be the number of rolls until (and including) the first roll of a 6, and define the random variable X to be the number of 1's rolled before the first 6 is rolled. Show that Pr(X = j i Y = 2'), as j ranges over its possible values, is the probability mass function of a binomially distributed random variable and determine its parameters n and p