Alice and Bob are running for office. Alice receives a votes and Bob receives b votes, where a>b. The votes are counted one at a time. What is the probability that sometime during the counting Bob is ahead of Alice?
The ballot theorem tells you the probability that Alice is strictly ahead of Bob. However, this question essentially asks the opposite. Would the answer just be 1 minus the probability that Alice is strictly ahead of Bob? Or am I oversimplifying this? Any help would be appreciated! Thank you!