the two - way table shows the ages of the players on different soccer teams.\n| | team a | team b | team c |…

the two - way table shows the ages of the players on different soccer teams.\n| | team a | team b | team c | team d | total |\n|--|--|--|--|--|--|\n| 8 years old | 4 | 6 | 8 | 3 | 21 |\n| 9 years old | 9 | 4 | 3 | 7 | 23 |\n| 10 years old | 2 | 3 | 5 | 4 | 14 |\n| total | 15 | 13 | 16 | 14 | 58 |\nwhich statement is true?\nthe probability that a randomly selected player on team a is 8 years old is $\frac{4}{21}$.\nthe probability that a randomly selected 8 - year - old player is on team c is $\frac{16}{21}$.\nthe probability that a randomly selected player on team c is 10 years old is $\frac{5}{16}$.\nthe probability that a randomly selected 10 - year - old player is on team b is $\frac{13}{58}$.

the two - way table shows the ages of the players on different soccer teams.\n| | team a | team b | team c | team d | total |\n|--|--|--|--|--|--|\n| 8 years old | 4 | 6 | 8 | 3 | 21 |\n| 9 years old | 9 | 4 | 3 | 7 | 23 |\n| 10 years old | 2 | 3 | 5 | 4 | 14 |\n| total | 15 | 13 | 16 | 14 | 58 |\nwhich statement is true?\nthe probability that a randomly selected player on team a is 8 years old is $\frac{4}{21}$.\nthe probability that a randomly selected 8 - year - old player is on team c is $\frac{16}{21}$.\nthe probability that a randomly selected player on team c is 10 years old is $\frac{5}{16}$.\nthe probability that a randomly selected 10 - year - old player is on team b is $\frac{13}{58}$.

Answer

Explanation:

Step1: Recall probability formula

Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Step2: Analyze first option

For the probability that a randomly - selected player on Team A is 8 years old, 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 is $\frac{4}{15}$, not $\frac{4}{21}$.

Step3: Analyze second option

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 is $\frac{8}{21}$, not $\frac{16}{21}$.

Step4: Analyze third option

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 $\frac{5}{16}$.

Step5: Analyze fourth option

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 is $\frac{3}{14}$, not $\frac{13}{58}$.

Answer:

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