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.....................................

Respuesta :

Answer:

0.3692

0.0785

0.5320

0.6308

0

0.2432

0.1468

Explanation:

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

[tex]P(G) = \frac{127}{344}\\P(G) = 0.3692[/tex]

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

[tex]P(S\cap R) = \frac{27}{344}\\P(S\cap R) = 0.0785[/tex]

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:

[tex]P(B\cup U)=\frac{109+35+39}{344}\\P(B\cup U)=0.5320[/tex]

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

[tex]P(S\cup B)=\frac{108+109}{344}\\P(S\cup B)=0.6308[/tex]

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

[tex]P(G\cap S)=0[/tex]

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

[tex]P(S|J)=\frac{9}{37}\\P(S|J)=0.2432[/tex]

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

[tex]P(A|B)=\frac{16}{109}\\P(A|B)=0.1468[/tex]