Question 266331
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
------------------------------------------------------------- 

b. Find the probability that the winner was from the U.S. given that she or he won a gold medal.
Prob = 35/133
-------------------------------------------------------------

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)
-------------------------------------------
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.
====================================================================
Cheers,
Stan H.
===================================