Let's analyze each statement one by one using the data provided:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline \text{} & \text{Gold} & \text{Silver} & \text{Bronze} & \text{Total} \\
\hline \text{United States} & 46 & 29 & 29 & 104 \\
\hline \text{China} & 38 & 27 & 23 & 88 \\
\hline \text{Russia} & 24 & 26 & 32 & 82 \\
\hline \text{Great Britain} & 29 & 17 & 19 & 65 \\
\hline \text{Total} & 137 & 99 & 103 & 339 \\
\hline
\end{array}
\][/tex]
1. The probability that a randomly selected silver medal was awarded to Great Britain is [tex]\(\frac{17}{99}\)[/tex]:
- The total number of silver medals is 99.
- The number of silver medals awarded to Great Britain is 17.
[tex]\[
\text{Probability} = \frac{17}{99} \approx 0.1717
\][/tex]
This statement is true.
2. The probability that a randomly selected medal won by Russia was a bronze medal is [tex]\(\frac{32}{103}\)[/tex]:
- The total number of medals won by Russia is 82.
- The number of bronze medals won by Russia is 32.
[tex]\[
\text{Probability} = \frac{32}{82} \approx 0.3902
\][/tex]
The ratio [tex]\(\frac{32}{103}\)[/tex] is incorrect. The correct probability is [tex]\(\frac{32}{82}\)[/tex]. Thus, this statement is false.
3. The probability that a randomly selected gold medal was awarded to China is [tex]\(\frac{88}{137}\)[/tex]:
- The total number of gold medals is 137.
- The number of gold medals awarded to China is 38.
[tex]\[
\text{Probability} = \frac{38}{137} \approx 0.2774
\][/tex]
The ratio given ([tex]\(\frac{88}{137}\)[/tex]) is incorrect. The correct values are used here. Therefore, this statement is false.
4. The probability that a randomly selected medal won by the United States was a silver medal is [tex]\(\frac{10}{33}\)[/tex]:
- The total number of medals won by the United States is 104.
- The number of silver medals won by the United States is 29.
[tex]\[
\text{Probability} = \frac{29}{104} \approx 0.2788
\][/tex]
The ratio ([tex]\(\frac{10}{33}\)[/tex]) is incorrect. The correct probability is [tex]\(\frac{29}{104}\)[/tex]. Thus, this statement is false.
In summary, the only true statement is the first one:
The probability that a randomly selected silver medal was awarded to Great Britain is [tex]\(\frac{17}{99}\)[/tex].
