Consider a game in which a fair coin is flipped an a fair six sided die is rolled. A player wins if the number on the die is smaller than or equal to 2 , or if the coin is a tail and the number on the die is a 6. How many outcomes are there in the sample space and what is the probability That the player loses any particular game?
My stab w/ this stuff (which I'm not that good at but preparing for w/ GRE prep)
Probability of getting $\leq 2$ on die: $2/6$
Probability of getting a tail AND a 6 on the die: $1/12$ ($1/2$ for coin toss $\cdot 1/6$ for die roll)
Total probability of win: $2/6 + 1/12 = 5/12$. Thus, probability to lose $= 7/12$.
Someone correct me if I messed that up.