You keep on rolling a pair of dice and let X be the number of rolls needed until you get a sum of 7 or 11 for the second time. Determine:
  1. P(7 or 11 on one roll)
  2. The expected number of rolls until you get the second 7 or 11 sum.
  3. P(X = 12)
  4. \(\displaystyle P(X \ge 4)\)
Solution.