Question

the two - way table shows the ages of the players on different soccer teams.

	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

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}\\).

Explanation:

Step1: Analyze Option 1

For the probability that a randomly selected player on Team A is 8 years old, we use the formula for conditional probability. The number of 8 - year - old players on Team A is 4, and the total number of players on Team A is 15. So the probability should be $\frac{4}{15}$, not $\frac{4}{21}$. So this option is incorrect.

Step2: Analyze Option 2

For the probability that a randomly selected 8 - year - old player is on Team C, the number of 8 - year - old players on Team C is 8, and the total number of 8 - year - old players is 21. So the probability should be $\frac{8}{21}$, not $\frac{16}{21}$. So this option is incorrect.

Step3: Analyze Option 3

For the probability that a randomly selected player on Team C is 10 years old, the number of 10 - year - old players on Team C is 5, and the total number of players on Team C is 16. So the probability is $\frac{5}{16}$. This option is correct.

Step4: Analyze Option 4

For the probability that a randomly selected 10 - year - old player is on Team B, the number of 10 - year - old players on Team B is 3, and the total number of 10 - year - old players is 14. So the probability should be $\frac{3}{14}$, not $\frac{13}{58}$. So this option is incorrect.

Answer:

The probability that a randomly selected player on Team C is 10 years old is $\frac{5}{16}$ (the third option).