Brain Teasers Optical Illusions Puzzle Hunts Codes & Ciphers Mechanical Puzzles
Personal Links
Browse Teasers
Search Teasers

Random Numbers With Constraints

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


Puzzle ID:#14822
Fun:*** (2.51)
Difficulty:*** (2.2)
Submitted By:j72883*
Corrected By:Sunrose




One of ten different furbies was randomly placed into each box of some type of cereal. If a mother decided to buy this cereal for her children until she obtained at least one of each of the ten different furbies, what is the number of boxes of cereal that she is expected to purchase?


This is a problem that uses elementary probability. We know that the probability of selecting a different toy is 1/10. But, when we purchase that first box of cereal, we have a 100% chance of getting a toy that we don't have. Applying a probability distribution, we are expected to purchase 1/1 boxes of cereal initially. Next, we have a 90% chance of getting a toy that we don't have, so total we purchase 1/1 + 1/.9 so far. The probability of getting a toy that we don't have thus decreases with each successive purchase, down to a 10% chance of getting one that we don't have once we've gotten all the others. Thus, we are expected to purchase:
1/1 + 1/.9 + 1/.8 + 1/.7 + 1/.6 + 1/.5 + 1/.4 + 1/.3 + 1/.2 + 1/.1 boxes of cereal for a total of 29.29.

She will probably need to buy 30 boxes before she gets one of each toy.


What Next?


See another brain teaser just like this one...

Or, just get a random brain teaser

If you become a registered user you can vote on this brain teaser, keep track of
which ones you have seen, and even make your own.


Back to Top

Online Now
8 users and 574 guests

Users In Chat
Follow Braingle!
Fold 'N Fly Paper Airplanes
Easy to follow folding instructions and videos.
Copyright © 1999-2017 | FAQ | Widgets | Links | Green | Subscribe | Contact | Privacy | Conditions | Advertise | Braingle Time: 7:27 pm
Sign In Create a free account