You have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7.
What is the probability that you get a sum of 4 before the sum of 7?  Choices
A) 1/6 B) 5/7 C) 2/8 D) 3/7 E) 2/5
E   2/5   Explanation:   This problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means.   Let us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7.   Thus, the probability that we get the sum of 4 before the sum of 7 will be:   4/(4+6) = 4/10 = 2/5.
<result>E</result>
You have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7.
What is the probability that you get a sum of 4 before the sum of 7?