I flip M coins, my opponent flips N coins. Who has more heads wins. Is there a closed form for probability?
In this game, I flip M fair coins and my opponent flips N coins. If I get more heads from my coins than my opponent, I win, otherwise I lose. I wish to know the probability that I win the game. I ...
Find the probability that splitting the unit interval into three random segments results in the sides of a triangle.
I found the question here. The precise problem is The unit interval is broken at two randomly chosen points along its length. Show that the probability that the lengths of the resulting three ...
Sorry to bother you, but I guess that this question is not appropriate for MO, so I repost it here hoping that someone could give me a clue. I would like to have an estimate for the series $$P(t) = ...
I am wondering if there is a closed form for finding the expected value or variance for a conditional exponential distribution. For example: $$ E(X|x > a) $$ where X is exponential with mean ...
Probability that a sequence of x coin flips will contain TH. How exactly would I approach this problem? Just need hints to direct me in the right direction.
Suppose we have $N$ kinds of colored balls, and there are an infinite number of each kind. Now we'd like to draw $m(m>N)$ balls from them. How to calculate the probability P(m,n), which is the ...
So, I played a game of Risk the other day for the first time since I was very little. I was frustrated to discover that I couldn't compute (at least not in my head) whether the attacker or the ...