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Through the Hoop

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

 

Puzzle ID:#44011
Fun:*** (2.37)
Difficulty:*** (2.7)
Category:Probability
Submitted By:javaguru*us**
Corrected By:MarcM1098

 

 

 



A 1-inch thick steel rod is bent into a perfectly round hoop with an interior diameter of two feet. The hoop is positioned with the opening parallel to the ground. Four inch balls are dropped from above randomly.

Is a ball more likely to hit the hoop or go through the hoop without hitting it?

Bonus question: What size hoop would you need in order to have the probability of a ball going through the hoop without hitting it equal the probability of hitting the hoop?





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Comments

markmonninAus*
Feb 02, 2009

Nice challenge. I forgot to include the width of the rod in my calculations.
melzerhAus*
Feb 02, 2009

I guess 66.6%?
opqpop
Oct 15, 2010

pretty good
eighsseAus*
Jul 27, 2013

I was thinking I screwed up the algebra because for some reason I was thinking the square root of 2 was less than 1 (not thinking much...duh), so I thought I was going to come up with a negative number. So I gave up on that and did trial and error til I knew it had to be just slightly over 14. So...yeah...mostly got it. Lol.

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