The Ballot Box

[irchans]

I read the following related questions in a probability book. I need the binomial theorem to solve #2, but I keep thinking there is a simpler solution.


#1 "In an election, two candidates, Albert and Benjamin, have in a ballot box a and b votes respectively, a> b, for example, 3 and 2. If ballots are randomly drawn and tallied, what is the chance that at least once after the first tally the candidates have the same number of tallies?"

#2 "Players A and B match pennies N times. They keep a tally of their gains and losses. After the first toss, what is the chance that at no time during the game will they be even?"





From "Fifty Challenging Problems in Probability" by Frederick Mosteller