Strat

phone interview with 5 mins bg discussion, all the rest are bts and programming questions

1) I have a bag with 100 white balls, randomly draw one and mark it
black if it's white, put
it back. What's the expectation of number of draws that all ball are
marked black?
(1 + 100/99 + 100/98 + ... + 100/1) How to approximate this number?

2) A bug is on the corner of a cube, what's the expectation of number
of steps that the bug
take to go to the opposite corner? One step means the bug from one
vertex to its neighbor
vertex.
( x denote the expectation of what we want, y denote the expectation
of steps take from vertexes 2
steps away from the destination, z denote the expectation of steps
from vertexes 1 step away from
destination. x = 1+y, y=1+1/3*x+2/3*z, z=1+1/3*1+2/3*y, so x =10)