A fair die is tossed successively. Let X denote the number of tosses until each of the six possible outcomes occurs at least once. Find the probability mass function of X. Hint: For 1 ≤ i ≤ 6, let E i...

A fair die is tossed successively. Let X denote the number of tosses until each of the six possible outcomes occurs at least once. Find the probability mass function of X. Hint: For 1 ≤ i ≤ 6, let E_i
be the event that the outcome i does not occur during the first n tosses of the die. First calculate P (X > n) by writing the event X > n in terms of E₁, E₂, ... , E₆.