MathDB

John is flipping his favorite bottle, which currently contains

10

ounces of water. However, his bottle is broken from excessive flipping, so after he performs a flip, one ounce of water leaks out of his bottle. When his bottle contains k ounces of water, he has a

\frac{1}{k+1}

probability of landing it on its bottom. What is the expected number of number of flips it takes for John’s bottle to land on its bottom ?

Problem Statement