The 1st statement i.e. "The probability that a randomly selected silver medal was awarded to Great Britain is StartFraction 17 Over 99 EndFraction" is true.

Step-by-step explanation:

The table:

Gold Silver Bronze Total

United States 46 29 29 104

China 38 27 23 88

Russia 24 26 32 82

Great Britain 29 17 19 65

Total 137 99 103 339

Let S be the sample space and E be the event and P(E) by the probability of a certain event.

1st Statement: The probability that a randomly selected silver medal was awarded to Great Britain is StartFraction 17 Over 99 EndFraction.

As the total number of silver medals are = n(S) = 99

The number of silver medals won by Great Britain = n(E) = 17

P(E) = n(E)/n(S) = 17/99

Hence, the probability that a randomly selected silver medal was awarded to Great Britain is 17/99.

So, the 1st statement i.e. "The probability that a randomly selected silver medal was awarded to Great Britain is StartFraction 17 Over 99 EndFraction" is true.

2nd Statement: The probability that a randomly selected medal won by Russia was a bronze medal is StartFraction 32 Over 103 EndFraction.

As the total number of medals won by Russian are = 82 = n(S) = 82

The number of bronze medals won by Russia are = n(E) = 32

P(E) = n(E)/n(S) = 32/82 = 16/41

Hence, the probability that a randomly selected medal won by Russia was a bronze medal is 16/41.

So, the 2nd statement i.e. "The probability that a randomly selected medal won by Russia was a bronze medal is StartFraction 32 Over 103 EndFraction" is NOT true.

3rd Statement: The probability that a randomly selected gold medal was awarded to China is StartFraction 88 Over 137 EndFraction.

As the total number of gold medals are = n(S) = 137

The number of gold medals won by China are = n(E) = 38

P(E) = n(E)/n(S) = 38/137

Hence, the probability that a randomly selected gold medal was awarded to China is 38/137.

So, the 3rd statement i.e. "The probability that a randomly selected gold medal was awarded to China is StartFraction 88 Over 137 EndFraction" is NOT true.

4th Statement: The probability that a randomly selected medal won by the United States was a silver medal is StartFraction 104 Over 339 EndFraction.

As the total number of medals won by United States are = n(S) = 104

The number of silver medals won by United States are = n(E) = 29

P(E) = n(E)/n(S) = 29/104 = 29/104

Hence, The probability that a randomly selected medal won by the United States was a silver medal is 29/104.

So, the 4th statement i.e. "The probability that a randomly selected medal won by the United States was a silver medal is StartFraction 104 Over 339 EndFraction." is NOT true.

Keywords: Probability, event

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