Posted: February 2nd, 2016

How many days (on average) will it take until all 50 friends are infected?

Problem: A computer has contracted a virus that spreads through email. Alice, the user of this computer has 50 friends: each day she picks one friend randomly (i.e. with equal probability p = 1/50) and sends him an email which unfortunately contains the virus.

Q1. How many days (on average) will it take until all 50 friends are infected? (Note that the same user can be picked on more than one days, in which case no new infection happens that day)
Q2. Assume that 3 months after Alice’s computer is initially infected, the antivirus company discovers the virus and offers a patch that cleans it up (so no further infections). How many of Alice’s friends will already be infected in these 3 months?