This book is one of the best probability books written. The explanations are very clear while at the same time the material covered is more advanced and interesting that what is commonly presented in undergraduate textbooks on probability. The problems are a real treasure, in that they are very interesting and challenging. Earlier I was working with a few students who are taking the MIT course 18.440 that was using this book. As they worked through the book, I worked the problems also and wrote up my solutions. When I made these solutions, I was working with the seventh edition of the book. I don't think there are substantial differences between later/earlier editions, however.
After about 10 years of giving this material away for free (in PDF format) I've decided to try to sell copies of it on Amazon. Please look here for the most recent version of the solution manual.
Update 2019-12-29: After many years I have updated these solutions to include all of the feedback I've receieved over the years. If you are interested in purchasing the current PDF version you can do so for $39.00 (US dollars) via PayPal (see the link below). Note: After you buy with PayPal you will be automatically directed to a web page where you can immediately download the solution manual.
Rather than use a calculator or do any numerical calculations by hand, I used Matlab in many cases. You can find any scripts or functions (often very short and quite trivial) that I created for a given problem in the links below.Code For Various Chapters: