Question: Cosmic wimpout. In this game five dice are rolled. four of the dice have the same set of symbols and numbers on their faces the numbers are 5 and 10, and let us call the symbols A, B, C, and D. the fifth die is the same, except symbol D is replaced by a different symbol w, indicating a wild roll, in one version of the game, the following kinds of rolls count for a score:
- Any roll that show one or more numbers:
- Any roll that shows a triple of symbols, where the wild symbol w can count as any symbol you like, e.g. WAABC scores a triple, the W counting as A:
- a roll that shows W together with one of each of the other symbols A, B, C, and D.
- any other combination fails to score, and is called a wimpout. calculate the probability of a Wimpout.