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

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 Team A, total players = 15. Number of 8 - year - old players on Team A = 4. Probability that a randomly selected player on Team A is 8 years old is $\frac{4}{15}$, not $\frac{4}{21}$.

Step3: Analyze second option

Total 8 - year - old players = 21. Number of 8 - year - old players on Team C = 8. Probability that a randomly selected 8 - year - old player is on Team C is $\frac{8}{21}$, not $\frac{16}{21}$.

Step4: Analyze third option

For Team C, total players = 16. Number of 10 - year - old players on Team C = 5. Probability that a randomly selected player on Team C is 10 years old is $\frac{5}{16}$.

Step5: Analyze fourth option

Total 10 - year - old players = 14. Number of 10 - year - old players on Team B = 3. Probability that a randomly selected 10 - year - old player is on Team B is $\frac{3}{14}$, not $\frac{13}{58}$.

Answer:

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