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 Probability and Statistics
 10 traffic lights
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shelby
New Member

USA
1 Posts

Posted - 10/17/2012 :  23:02:26  Show Profile  Reply with Quote
if there are 10 traffic lights what is the probability that at lest one is red? I am having trouble even beginning this one
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royhaas
Moderator

USA
3059 Posts

Posted - 10/18/2012 :  08:56:11  Show Profile  Reply with Quote
The probability that none of them are red will depend on how many colors are not red.
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 10/18/2012 :  16:30:46  Show Profile  Reply with Quote
If there were just there are just two colors (say green and red), then there are 2^10 (or, that is 1024) configurations total.
The part of the problem that says "at least one is red" would mean that you just eliminate the ONE configuration GGGGGGGGGG (all green) and that makes the answer 1023/1024.
For three colors (red yellow green) is probably what this question is dealing with. The same procedure can be done by changing the "2" to a "3".
Now, I have another comment which the author of the problem also did not consider. Does each light stay on for the same time before changing to a different color. That would make a difference in the answer also. For example, if Green stayed on for, say 3 minutes and red for only 5 seconds and yellow for only 1 second (extreme case) but that would make the probability VERY low. Of course, this is not to be considered in this problem.
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