Suppose all nodes are honest, blocks will occasionally get orphaned. If two miners Alice and Bob discover blocks nearly simultaneously, neither will have time to hear about the others block before broadcasting her/his own one.

a) Whose block will end up on the consensus branch? Why?

b) What factors affect the rate of orphan blocks?

c) If Alice hears about Bobs block just before she is going to broadcast hers, will Alice waste her effort of mining? Why?

d) Assume the total hash power of the network is a constant, what is the probability that a block will be found in the next round (i.e., 10 minutes)?

e) Suppose a merchant, Bob, wants to have a policy that orders will be completed within x minutes after receipt of payment. What value of x should Bob choose such that with 99% confidence 6 blocks will be found within x minutes?

Hints: Discovery of blocks is a Poisson process.