Question 266331: The medal distribution from the 2004 Summer Olympic Games for the top 23 countries is shown below:
Gold Silver Bronze
U.S. 35 39 29
Russia 27 27 38
China 32 17 14
Australia 17 16 16
Others 133 136 153
Choose 1 medal winner at random.
a. Find the probability that the winner won the gold medal, given that the winner was from the U.S.
b. Find the probability that the winner was from the U.S. given that she or he won a gold medal.
c. Are the events "medal winner is from U.S." and "gold medal won" independent? Explain.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The medal distribution from the 2004 Summer Olympic Games for the top 23 countries is shown below:
Gold Silver Bronze Total
U.S. 35 39 29 104
Russia 27 27 38 92
China 32 17 14 63
Australia 17 16 16 49
Others 133 136 153 422
----------------------------------------730
Choose 1 medal winner at random.
a. Find the probability that the winner won the gold medal, given that the winner was from the U.S.
P(gold|US win) = P(gold and US)/P(uS win) = 35/104
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b. Find the probability that the winner was from the U.S. given that she or he won a gold medal.
Prob = 35/133
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c. Are the events "medal winner is from U.S." and "gold medal won" independent? Explain.
Check to see if P(A|B) = P(A)*P(B)
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P(from U.S.| gold won) = P(from U.S. AND gold won)/P(gold won)
= (35/730)/(133/730) = 35/730
P(from U.S.)*P(gold won) = (104/730)(133/730)
Ans: The results are not equal so the factors are no independent.
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Cheers,
Stan H.
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