Another Sweet Problem
Alice just gave bob a box filled with 9 candies. Initially, each of the 9 candies is wrapped. They decided to play the following game,
1) Bob chooses a wrapper from the box randomly one by one (assuming he can't differentiate between full and empty wrappers by touching).
2) If the wrapper contains a candy, bob eats it and puts the wrapper back in the box.
3) If wrapper is empty and there are any candies remaining, Alice wins.
4) If bob eats all the 9 candies without getting a single empty wrapper, Bob wins.
Now, suppose p/q is the chance of bob winning the game (q and p are co-prime), submit your answer as p + q.
You may want to use a fraction calculator.
The answer is 4787449.
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1 solution
A brief analysis using multiplicative rule would show that for 'n' candies, probability of getting all of them without getting a single wrapper (given that empty wrappers are put back into the box) turns out to be
p(n)= n n n !
the value for p(9) in form of fraction can simply be calculated using some online calculator or programming language.