Probability!

At last, there's something which I like about my modules~ Probability and statistics! Used to love this portion of maths more than anything else. Somehow I feel that Statistics is another thing when compared to pure mathematics or mechanics, simply because there's a story behind every question, and solving the problems seems just like completing the story which was left unfinished by the examiner. Too bad this assignment came when I aren't really in the mood to revise the formulas again, but I still miss Poisson and normal and binomial and all, not the mention the bell shaped dummy~ Sigh ... why can't I just study something which I like and I am capable of? Alrigh alright, enough of snaring. Here's one sample question from the assignment which I believe everyone is capable of solving.

In a certain game, you may roll a normal, unbiased die and receive $1 for each spot on the face which lands face up.
a) What is the fair price for this game?
b) The game is now modified such that you may chose to have a second throw and use the spots from this throw to receive your prize money. For which cases would you chose to roll again?
c) What would be the expected prize money for this game?

Surely, this questions is much simpler than those which I did during A levels (anyone recalled?), and you certainly won't expect such questions to appear in a unveristy assignment... but who cares?I still miss probability and statistics as always~

Answer: a) 3.5 b) 1, 2, 3 c) 4.25 (These are my answers, and they might not be correct)