Question

the two - way table shows the medal count for the top - performing countries in the 2012 summer olympics.

	united states	china	russia	great britain	total
silver	29	27	26	17	99
bronze	29	23	32	19	103
total	104	88	82	65	339

which statement is true?

• the probability that a randomly selected silver medal was awarded to great britain is $\frac{17}{99}$.
• the probability that a randomly selected medal won by russia was a bronze medal is $\frac{32}{103}$.
• the probability that a randomly selected gold medal was awarded to china is $\frac{88}{137}$.
• the probability that a randomly selected medal won by the united states was a silver medal is $\frac{104}{339}$.

Explanation:

To determine the correct statement, we analyze each option using the two - way table data:

Option 1: Probability that a randomly selected silver medal was awarded to Great Britain

• Total number of silver medals: From the "Silver" row and "Total" column, we have \(n(\text{silver}) = 99\).
• Number of silver medals awarded to Great Britain: From the "Silver" row and "Great Britain" column, we have \(n(\text{silver and Great Britain})=17\).
• The probability \(P=\frac{\text{Number of silver medals for Great Britain}}{\text{Total number of silver medals}}=\frac{17}{99}\). This statement is correct. But let's check the other options for completeness.

Option 2: Probability that a randomly selected gold medal was awarded to China

• Total number of gold medals: From the "Gold" row and "Total" column, we have \(n(\text{gold}) = 137\).
• Number of gold medals awarded to China: From the "Gold" row and "China" column, we have \(n(\text{gold and China}) = 38\).
• The probability \(P=\frac{38}{137}

eq\frac{88}{137}\). So this statement is incorrect.

Option 3: Probability that a randomly selected medal won by Russia was a bronze medal

• Total number of medals won by Russia: From the "Total" row and "Russia" column, we have \(n(\text{medals for Russia})=82\).
• Number of bronze medals won by Russia: From the "Bronze" row and "Russia" column, we have \(n(\text{bronze and Russia}) = 32\).
• The probability \(P=\frac{32}{82}

eq\frac{32}{103}\). So this statement is incorrect.

Option 4: Probability that a randomly selected medal won by the United States was a silver medal

• Total number of medals won by the United States: From the "Total" row and "United States" column, we have \(n(\text{medals for US}) = 104\).
• Number of silver medals won by the United States: From the "Silver" row and "United States" column, we have \(n(\text{silver and US})=29\).
• The probability \(P=\frac{29}{104}

eq\frac{104}{339}\). So this statement is incorrect.

The correct statement is "The probability that a randomly selected silver medal was awarded to Great Britain is \(\frac{17}{99}\)".

So the answer is the first option: "The probability that a randomly selected silver medal was awarded to Great Britain is \(\frac{17}{99}\)".

Answer:

To determine the correct statement, we analyze each option using the two - way table data:

Option 1: Probability that a randomly selected silver medal was awarded to Great Britain

• Total number of silver medals: From the "Silver" row and "Total" column, we have \(n(\text{silver}) = 99\).
• Number of silver medals awarded to Great Britain: From the "Silver" row and "Great Britain" column, we have \(n(\text{silver and Great Britain})=17\).
• The probability \(P=\frac{\text{Number of silver medals for Great Britain}}{\text{Total number of silver medals}}=\frac{17}{99}\). This statement is correct. But let's check the other options for completeness.

Option 2: Probability that a randomly selected gold medal was awarded to China

• Total number of gold medals: From the "Gold" row and "Total" column, we have \(n(\text{gold}) = 137\).
• Number of gold medals awarded to China: From the "Gold" row and "China" column, we have \(n(\text{gold and China}) = 38\).
• The probability \(P=\frac{38}{137}

eq\frac{88}{137}\). So this statement is incorrect.

Option 3: Probability that a randomly selected medal won by Russia was a bronze medal

• Total number of medals won by Russia: From the "Total" row and "Russia" column, we have \(n(\text{medals for Russia})=82\).
• Number of bronze medals won by Russia: From the "Bronze" row and "Russia" column, we have \(n(\text{bronze and Russia}) = 32\).
• The probability \(P=\frac{32}{82}

eq\frac{32}{103}\). So this statement is incorrect.

Option 4: Probability that a randomly selected medal won by the United States was a silver medal

• Total number of medals won by the United States: From the "Total" row and "United States" column, we have \(n(\text{medals for US}) = 104\).
• Number of silver medals won by the United States: From the "Silver" row and "United States" column, we have \(n(\text{silver and US})=29\).
• The probability \(P=\frac{29}{104}

eq\frac{104}{339}\). So this statement is incorrect.

The correct statement is "The probability that a randomly selected silver medal was awarded to Great Britain is \(\frac{17}{99}\)".

So the answer is the first option: "The probability that a randomly selected silver medal was awarded to Great Britain is \(\frac{17}{99}\)".