In a game with 2 dice, you win if you get a sum of 7 or 11 or roll doubles.
a. what are the chances against winning this game?
b. explain how you solved this question.

Question

In a game with 2 dice, you win if you get a sum of 7 or 11 or roll doubles.
a. what are the chances against winning this game?
b. explain how you solved this question.

mathmate · Answer

There are 6 ways to get a 7, and 2 ways to get an 11, all out of 36 outcomes.
Chances of winning game is therefore (7+2)/36=1/4, and chances against winning is 1-1/4=3/4 (or odds 3:1)
Either count by enumeration, or by drawing a 6x6 table and counting the outcomes.