Originally Posted by

**RespeckKnuckles** I hope these aren't too hard for the basic statistics forum, but some friends and I are disagreeing on the answers to these two questions:

1) Show that if two dice are loaded with the same probability distribution, then the probability of doubles is at least 1/6.

2) If P2 is the probability of a 2 showing and we are told that at least one 2 has shown, what is the probability that upon looking at the pair of dice the sum will be 4?

Now for each question:1) My initial solution to this was to show that the probability of doubles on die with even distributions are 1/6, so any variation in the distribution leads to a smaller number. But I can't quite prove this algebraically and I'm stuck. Is my approach wrong?