binomial (undefined function) I’m trying to answer this question using binomial pmf.
1-i have a shelf contains 4 ( 500 pages book) what is the probability that when i select 1 book i get a book consists at least of 200 pages ? 
2- in another case where is the shelf contains 4 ( 100 pages book ). what is the probability of selecting 1 book that in each there is at least 200 pages 
i know the answer is pretty much straight forward ( 1,0) for 1 and to respectively.
however, how can i formulate this using probability theory laws.
i have tried hypergeometric pmf but i ended up getting undefined value of 0/0 for the second part of the question.
any help is highly appreciated :))
 A: Suppose the books are labeled $a,b,c,d$.  Let $A,B,C,D$ represent the event of taking books $a,b,c,d$ respectively.  Let our sample space be all ways of selecting one book.  Then clearly $A,B,C,D$ form a partition of the sample space.  (I.e. $P(A\cup B\cup C\cup D)=P(A)+P(B)+P(C)+P(D)=1$).
Let $K$ represent the event that the book selected has at least 200 pages.
In the first example, note that $K\cap A=A$ since if you selected book $A$, since $A$ has 500 pages it therefore has at least 200 pages.  Similarly for the other books.  As such $P(K)=P(K\cap \Omega) = P(K\cap (A\cup B\cup C\cup D)) = P((K\cap A)\cup (K\cap B)\cup (K\cap C)\cup (K\cap D)) = P(A\cup B\cup C\cup D)=1$
Similarly in the second example, $K\cap A=\emptyset$ since selecting book $A$, which has 100 pages, does not satisfy the requirement that the book selected has at least 200 pages.  In a similar manner as before, we get $P(K)=0$.
The specific probability distribution used to select which book is completely irrelevant to the problem.
