In a certain game, a player wants to roll five dice and get as many l's as possible. Here is the scheme:
Round 1: The player rolls all five of the dice, and notices how many l's appear.
Round 2: The player sets the l's aside and only rolls the dice which did not show a 1 the first time.
Round 3: The player sets the l's aside from rounds 1 and 2 and only rolls the dice which still did not yet show a 1.
After three rounds, the player is tired so she stops. How many l's does she expect to have at this point?
(Consider one Bernoulli for each of the dice, so E(X1 + ... + X5) = E(X1) + ... + E(X5).)