Question

the two - way table shows the ages of the players on different soccer teams. which statement is true? \
\
the probability that a randomly selected player on team a is 8 years old is \\(\frac{4}{21}\\). \
the probability that a randomly selected 8 - year - old player is on team c is \\(\frac{16}{21}\\). \
the probability that a randomly selected player on team c is 10 years old is \\(\frac{5}{16}\\). \
the probability that a randomly selected 10 - year - old player is on team b is \\(\frac{13}{58}\\). \
\

	team a	team b	team c	team d	total	\
---	---	---	---	---	---	\
8 years old	4	6	8	3	21	\
9 years old	9	4	3	7	23	\
10 years old	2	3	5	4	14	\
total	15	13	16	14	58

Explanation:

To solve this, we analyze each statement by calculating the relevant probabilities using the two - way table.

Statement 1: The probability that a randomly selected player on Team A is 8 years old is $\frac{4}{21}$.

• The total number of players on Team A is the sum of the number of 8 - year - old, 9 - year - old, and 10 - year - old players on Team A. From the table, the number of 8 - year - old players on Team A is 4, the number of 9 - year - old players on Team A is 9, and the number of 10 - year - old players on Team A is 2. So, the total number of players on Team A is $4 + 9+2=15$.
• The number of 8 - year - old players on Team A is 4. The probability that a randomly selected player on Team A is 8 years old is the number of 8 - year - old players on Team A divided by the total number of players on Team A, which is $\frac{4}{15}

eq\frac{4}{21}$. So, this statement is false.

Statement 2: The probability that a randomly selected 8 - year - old player is on Team C is $\frac{16}{21}$.

• The total number of 8 - year - old players is 21 (from the "Total" row and "8 Years Old" column). The number of 8 - year - old players on Team C is 8.
• The probability that a randomly selected 8 - year - old player is on Team C is the number of 8 - year - old players on Team C divided by the total number of 8 - year - old players, which is $\frac{8}{21}

eq\frac{16}{21}$. So, this statement is false.

Statement 3: The probability that a randomly selected player on Team C is 10 years old is $\frac{5}{16}$.

• The total number of players on Team C is 16 (from the "Total" column and "Team C" row). The number of 10 - year - old players on Team C is 5.
• The probability that a randomly selected player on Team C is 10 years old is the number of 10 - year - old players on Team C divided by the total number of players on Team C, which is $\frac{5}{16}$. So, this statement is true.

Statement 4: The probability that a randomly selected 10 - year - old player is on Team B is $\frac{13}{58}$.

• The total number of 10 - year - old players is 14 (from the "Total" row and "10 Years Old" column). The number of 10 - year - old players on Team B is 3.
• The probability that a randomly selected 10 - year - old player is on Team B is the number of 10 - year - old players on Team B divided by the total number of 10 - year - old players, which is $\frac{3}{14}

eq\frac{13}{58}$. So, this statement is false.

The true statement is "The probability that a randomly selected player on Team C is 10 years old is $\frac{5}{16}$".

Answer:

To solve this, we analyze each statement by calculating the relevant probabilities using the two - way table.

Statement 1: The probability that a randomly selected player on Team A is 8 years old is $\frac{4}{21}$.

• The total number of players on Team A is the sum of the number of 8 - year - old, 9 - year - old, and 10 - year - old players on Team A. From the table, the number of 8 - year - old players on Team A is 4, the number of 9 - year - old players on Team A is 9, and the number of 10 - year - old players on Team A is 2. So, the total number of players on Team A is $4 + 9+2=15$.
• The number of 8 - year - old players on Team A is 4. The probability that a randomly selected player on Team A is 8 years old is the number of 8 - year - old players on Team A divided by the total number of players on Team A, which is $\frac{4}{15}

eq\frac{4}{21}$. So, this statement is false.

Statement 2: The probability that a randomly selected 8 - year - old player is on Team C is $\frac{16}{21}$.

• The total number of 8 - year - old players is 21 (from the "Total" row and "8 Years Old" column). The number of 8 - year - old players on Team C is 8.
• The probability that a randomly selected 8 - year - old player is on Team C is the number of 8 - year - old players on Team C divided by the total number of 8 - year - old players, which is $\frac{8}{21}

eq\frac{16}{21}$. So, this statement is false.

Statement 3: The probability that a randomly selected player on Team C is 10 years old is $\frac{5}{16}$.

• The total number of players on Team C is 16 (from the "Total" column and "Team C" row). The number of 10 - year - old players on Team C is 5.
• The probability that a randomly selected player on Team C is 10 years old is the number of 10 - year - old players on Team C divided by the total number of players on Team C, which is $\frac{5}{16}$. So, this statement is true.

Statement 4: The probability that a randomly selected 10 - year - old player is on Team B is $\frac{13}{58}$.

• The total number of 10 - year - old players is 14 (from the "Total" row and "10 Years Old" column). The number of 10 - year - old players on Team B is 3.
• The probability that a randomly selected 10 - year - old player is on Team B is the number of 10 - year - old players on Team B divided by the total number of 10 - year - old players, which is $\frac{3}{14}

eq\frac{13}{58}$. So, this statement is false.

The true statement is "The probability that a randomly selected player on Team C is 10 years old is $\frac{5}{16}$".