SOLUTION: n a complete graph with 12 nodes you choose the color for the edges in a following manner: You toss a coin for each edge. If the coin shows heads, you toss a three sided fair die.

Algebra ->  Probability-and-statistics -> SOLUTION: n a complete graph with 12 nodes you choose the color for the edges in a following manner: You toss a coin for each edge. If the coin shows heads, you toss a three sided fair die.       Log On


   

Question 1174440: n a complete graph with 12 nodes you choose the color for the edges in a following manner: You toss a coin for each edge. If the coin shows heads, you toss a three sided fair die. If the die shows 1 you color the edge blue, if the die shows 2 you color the edge yellow and in case the die shows 3 you color the edge green. In case the coin shows tails, you toss a three sided fair die also. This time, if the die shows 1 or 2 the edge is colored yellow, while if it shows 3 the edge is colored red. Given that you just colored the edge yellow, find the probability that the coin toss resulted in “heads”? (Give the probability in the form of a fraction (example: 4/5)! )
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(heads; 1) --> blue
(heads; 2) --> yellow
(heads; 3) --> green
(tails; 1) --> yellow
(tails; 2) --> yellow
(tails; 3) --> red

Each of the 6 cases has probability (1/2)(1/3) = 1/6

3 of the cases with equal probability result in a yellow edge; in 1 of those 3 cases the coin toss was heads.

ANSWER: 1/3

More formally, using the definition of conditional probability...



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By the way....

I'm really curious about what that three sided die looks like....!