So my buddy claims that if I split a chocolate bar at random into two pieces, then the expected size of the larger piece is $\frac{3}{4}$ of the bar. I can't figure out how he came up with this value...
Can someone explain this? If you can, can you provide some kind of a proof?
p.s. it would be helpful to think of this chocolate bar as a 1D array :)
UPDATE
Imagine the candy bar is a world-famous chocolate bar, the ones that are broken into chunks. However, this special chocolate bar has n
chunks. If we broke the chocolate bar randomly along these chunks, what would the expected size of the larger chunk be? My buddy claims it to be $\leq{\frac{3}{4}}$.