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Jellybean Party Favors

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 

Puzzle ID:#44169
Fun:*** (2.25)
Difficulty:*** (2.89)
Category:Probability
Submitted By:javaguru*us**
Corrected By:javaguru

 

 

 



Rex is having a party and has prepared party favors for his guest. As each guest arrives they are given a small paper bag of licorice and cherry jellybeans. Each bag has the same number of jellybeans, but no two bags have the same combination of cherry and licorice jellybeans.

Altogether there are 42 bags of jellybeans and 41 jellybeans in each bag. What is the probability that the first three jellybeans a guest randomly removes from her bag are the same flavor?


Hint

The number of (licorice, cherry) in each bag are (41, 0), (40, 1), (39, 2), ... (1, 40), (0, 41).

The answer would be the same if there were 26 bags of 25 jellybeans each.

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