The random ant question is asked in this post.
I reproduce it below for completeness.
Question: $500$ ants are randomly put on a 1-foot string (independent uniform distribution for each ant between 0 and 1). Each ant randomly moves toward on end of the string (equal probability to the left or the right) at constant speed of 1 foot/minute until it falls of a t one end of the string. Also assume that the size of the ant is infinitely small. When two ants collide head-on, they both immediately change directions and keep on moving at 1 foot/min. What is the expected time for all ants to fall off the string?
The question above is equivalent to asking the expected value of the maximum of $500$ IID random variables with uniform
distribution between $0$ and $1$.
We know that the expected value of $\max(X_1,…,X_{500})$ where $X_1,…,X_{500}$ are IID, is $\frac{500}{501}$, as shown in another post.
However, the answer given to the random ant question is $\frac{499}{500},$ which I fail to decipher.
Best Answer
The guide that gives $\frac{499}{500}$ as an answer is wrong. You're right that it should be $\frac{500}{501}$.