Problem 1:
--- "no 0's or no 1's" shoud be "no 0's and no 1's"
--- BMU is used both as a set and as a type: you write both 
           "t is a BMU"    and    "t \in BMU". 
You probably want to stick to only one of the two phrasings. 
I'd prefer the set notation.
--- Part (b):  "inductive case" should be "inductive step"
--- the concatenation operator  \cdot  is sometimes used and sometimes
omitted. This may confuse students.


Problem 2:
--- You may want to put in italics the mention that the cards are
shuffled when originally put on the table.


Problem 3:
--- Shouldn't it start at a new page?
--- Typo: "Then number of cards"


Problem 4:
--- Shouldn't it start at a new page?


Problem 5:
--- Ok.