For a pair of dice you want to consider the events A = {rolling a 7 or 11} and B = {otherwise}...as in the first roll in the game of craps. Further, for notation purposes let’s take ABA (for example) to mean event A occurs on the first roll, event B occurs on the second roll, and event A occurs again on the third roll...in that order only. If you roll the dice 5 times, determine
  1. P(AABBB)
  2. P(BBBAA)
  3. The probability of getting A on exactly two rolls of the dice.
Solution.