Statistics : Solution Essays

There is a game called Under-or-Over Seven.  A pair of fair dice is rolled once and the resulting sum determines whether the player wins or loses his or her bet.  For example, the player can bet $1 that the sum will be under 7 — that is 2, 3, 4, 5, or 6.  For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals to or is greater than 7.  Similarly, the player can bet $1 that the sum will be over 7  — that is 8, 9, 10, 11, or 12.   Here the player wins $1 if the result is over 7, but loses $1 if the outcome is 7 or under.  A third method of play is to bet $1 on the outcome 7.  For this bet, the player wins $4 if the result of the roll is 7 and loses $1 otherwise.