the_hill1962
Advanced Member
USA
1469 Posts 
Posted  10/18/2012 : 16:30:46

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. 

