[irchans]

I got 2 b / (a + b) after I did a ridiculous amount of work.
Then I read a simple the simple solution below.





solution :

If the first vote is B, then there will be a tie.

b/ (a + b) = P(first vote is B)
= P(first vote is B and a tie occurs)

Suppose you have a voting sequence that has a tie and the first vote is not B. Switch all the A's and the B's up to the tie vote, then you get a voting sequence with the same number of A's and B's starting with a B. So,

P( first vote is A and a tie occurs ) =
P( first vote is B and a tie occurs ) = b/ (a + b)

Adding them together we get

P(tie occurring) = 2 b / (a + b)