Question

Country Gold Silver Bronze Totals United States 35 39 29 103 China 32 17 14 63 Russia 27 27 38 92 Australia 17 16 16 49 Japan 16 9 12 37 Totals 127 108 109 344 If a medal is picked at random from this group, find the probability that it was A gold medal....................................... A silver medal won by a Russian...................................... A bronze medal or won by the United States............................... A silver medal or a bronze medal...................................... A gold medal and a silver medal....................................... A silver medal given that it was won by Japan................................. A medal won by Australia given that it was bronze.....................................

Answer 1

0.3692

0.0785

0.5320

0.6308

0

0.2432

0.1468

Step-by-step explanation:

A gold medal - Number of gold medals divided by total number of medals:

`P(G) = (127)/(344)\\P(G) = 0.3692`

A silver medal won by a Russian - Number of silver medals won by Russia divided by total number of medals:

`P(S\cap R) = (27)/(344)\\P(S\cap R) = 0.0785`

A bronze medal or won by the United States - Number of total bronze medals added to silver and gold medals from USA, divided by total number of medals:

`P(B\cup U)=(109+35+39)/(344)\\P(B\cup U)=0.5320`

A silver medal or a bronze medal - Number of total silver plus total gold medals divided by total number of medals:

`P(S\cup B)=(108+109)/(344)\\P(S\cup B)=0.6308`

A gold medal and a silver medal - A medal can't be both gold and silver, the probability is zero:

`P(G\cap S)=0`

A silver medal given that it was won by Japan - Number of Japan silver medals divided total medals won by Japan:

`P(S|J)=(9)/(37)\\P(S|J)=0.2432`

A medal won by Australia given that it was bronze - Number of Australia bronze medals divided by total bronze medals:

`P(A|B)=(16)/(109)\\P(A|B)=0.1468`