The medal distribution from the 2000 summer olympic games isshown in the table.

Question

The medal distribution from the 2000 summer olympic games isshown in the table. Gold Silver Bronze United States 39 25 33 Russia 32 28 28 China 28 16 15 Australia 16 25 17    Others 186 205 235 Choose one medal winner at random i. Find the prob that the winner won the gold medal, giventhat the winner was from the United States? ii. Find the prob that the winner was from the United States,given that she or he won a gold medal? iii. Are the events "medal winner is from the U.S" and "goldmedel was won" independent? explain The medal distribution from the 2000 summer olympic games isshown in the table. Gold Silver Bronze United States 39 25 33 Russia 32 28 28 China 28 16 15 Australia 16 25 17    Others 186 205 235 Choose one medal winner at random i. Find the prob that the winner won the gold medal, giventhat the winner was from the United States? ii. Find the prob that the winner was from the United States,given that she or he won a gold medal? iii. Are the events "medal winner is from the U.S" and "goldmedel was won" independent? explain Gold Silver Bronze United States 39 25 33 Russia 32 28 28 China 28 16 15

Explanation / Answer

(i) P(gold medal | United States)= P(gold medal and UnitedStates)/P(United States) =39/(39+25+33)=0.402 (ii) P(United states| gold medal)= P(United states and goldmedal)/P(gold medal) =39/(39+32+28+16+186)= 0.1296 (iii) Since P(U.S) *P(gold medal) not equal P(U.S and gold medal),they are not independent.

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