A student passes through three traffic lights on the way to school. Each light i
ID: 3217216 • Letter: A
Question
A student passes through three traffic lights on the way to school. Each light is either red, yellow, or green. An experiment consists of observing the colors of the three lights. List all outcomes in the sample space. Let A be the event that all the colors are the same. List the outcomes in A. Let B be the event that all the colors are different. List the outcomes in B. Let C be the event that at least two lights are green. List the outcomes in C. List the outcomes in A intersection C. List the outcomes in A union B. List the outcomes in A intersection C^C. List the outcomes in A^C intersection C. Are events A and C mutually exclusive? Explain. Are events B and C mutually exclusive? Explain.Explanation / Answer
Solution:-
1) All the oucomes in the sample space are 27 listed below.
(RYG), (RGY), (RYY), (RGG), (RRG), (RGR), (RRY), (RYR), (RRR)
(YRG), (YGR), (YGG),(YRR), (YYR), (YRY), (YYG), (YGY), (YYY)
(GRY), (GYR), (GYY), (GRR), (GGR), (GRG), (GGY), (GYG), (GGG)
2) The outcomes in A are (RRR), (GGG), (YYY).
3) The outcomes that all colors are different are (RYG), (RGY), (GRY), (GYR),(YRG), (YGR).
4) The outcomes in C are (GGR), (GRG), (GGY), (GYG), (GGG), (RGG), (YGG)
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