There are 7 mysteries, 9 biographies, 2 reference books,and 10 picture books in the book bin at the library. What are the odds of drawing a mystery...

To figure out the probability (odds) of something happening, what you have to do is count up ALL the possibilities, and then count up how many of them involve the result you are looking for.

In this case, there are 28 different books, so there is a total of 28 possibilities of what book will be drawn from the bin.   Since 7 of the books are mysteries, 7 out of the 28 possibilities will be mysteries.  From a math standpoint, this is 7:28 or 7 out of 28.  Since 7 goes evenly into 28 (4 x 7 = 28), you can reduce it to 1:4 or 1 out of 4.  

It is important to remember that the probability is what would happen on average if you tried it many, many times.  You can't be sure that 1 of the first 4 books you actually pull on one try will be a mystery.  1 out of 4 is just the probable result.