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Whoever gets the most correct answers, or closest to the correct answers, for these questions, gets a free copy of Dreamweaver 8 All-in-One desk reference, retail value $45 Canadian.  Plus that person will get recognition from me as being really really smart.

1. A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data:

85% of the cabs in the city are Green and 15% are Blue.

A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time.

What is the probability that the cab involved in the accident was Blue rather than Green?  (Please feel free to estimate if you’d like.)

2. You have two ropes, two sticks, and a lighter. You know that if you light the rope, it will take one hour to burn.  However, it doesn’t necessarily burn at the same rate all hour long.  It might burn slowly for 55 minutes, then consume the rest of the rope in 5 minutes.

You need to know when exactly 15 minutes has elapsed.  How do you do it?

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Comments

 

 

1. If I'm reading this correctly, the witness is equally reliable identifying green or blue cabs, so the witness's assertion that the cab was Blue is 80% likely to be true. But given the different sample sizes I'm probably oversimplifying and maybe Bayesian formulas should be brought into play.

2. Can you make a sundial with one of the sticks, with enough markings around the outside to show quarter hours? Of course, you'd need to track the movement of the sun for a day to get the hours, so that's probably wrong.

 

Posted by Christina  at  11:01 pm on Nov. 27, 2006

 

 

 

1. Um, 80%?! That's what they tested right?

2. You didn't say you didn't have a watch, so time it? What would you want to burn rope for 15 minutes for anyway?

 

Posted by Kathryn  at  7:06 pm on Dec. 9, 2006

 

 

 

light three ends simultaneously.

First rope with both ends lit burns completely that is 30 minutes; because if it took 60 min. for it to burn completely if only one end is lit.

When rope 1 is burnt up, light remaining unlit end of rope 2.

When it meets the burning portion on rope 2, 15 minutes will have passed.

 

Posted by Rik Warren  at  8:02 am on May. 21, 2008

 

 

 

Yes, the rope question is answered right.

The cab question, the answer is: 41% lkely to be correct (so, more likely to be wrong). He'll be correct 12 out of 29 guesses. See: http://www.esmerel.com/circle/numeracy/accident.html

 

Posted by Travis Smith  at  2:21 pm on May. 21, 2008

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