Books similar to Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller I find the book Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller.
I would like to solve more probability problems whose levels are similar to book above. 
Does anyone have good suggestions?
 A: The closest to Mosteller's book is probably Yaglom's Challenging Mathematical Problems With Elementary Solutions: Combinatorial Analysis and Probability Theory. It was published around the same time, the problems have a similar flavor, and it doesn't require any knowledge of measure theory.
You may also be interested in Patrick's Intermediate Counting and Probability, as well as in the chapter "Combinatorics and Probability" of Andreescu's Putnam and Beyond.
A: I would also suggest the "Problems and solutions" section of the Americal Matematical Monthly journal. Quite frequently they suggest problems related to probability and statistics. According to me sometimes they have the same flavour as problems from the Mosteller's and Yaglom's book.  
Don't know whether there exists a separate archive of the "Problems and solutions" section. Yet, most of the issues are available here https://www.jstor.org/journal/amermathmont.
There is one book with the collection of problems from SIAM: Murray S. Klamkin - Problems in applied mathematics: selections from SIAM review-Society for Industrial and Applied Mathematics (1987) https://epubs.siam.org/doi/book/10.1137/1.9781611971729. It has the probability chapter, including some problems from Americal Matematical Monthly. Moreover, in some problems not related to probability, you can find unexpected comments related to probability.
