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?\no the probability that a randomly selected player on team a is 8 years old is $\frac{4}{21}$.\no the probability that a randomly selected 8 - year - old player is on team c is $\frac{16}{21}$.\no the probability that a randomly selected player on team c is 10 years old is $\frac{5}{16}$.\no the 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?\no the probability that a randomly selected player on team a is 8 years old is $\frac{4}{21}$.\no the probability that a randomly selected 8 - year - old player is on team c is $\frac{16}{21}$.\no the probability that a randomly selected player on team c is 10 years old is $\frac{5}{16}$.\no the 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 a player on Team A to be 8 - year - old, number of 8 - year - old players on Team A is 4 and total number of players on Team A is 15. Probability = $\frac{4}{15}\neq\frac{4}{21}$

Step3: Analyze second option

For an 8 - year - old player to be on Team C, number of 8 - year - old players on Team C is 8 and total number of 8 - year - old players is 21. Probability = $\frac{8}{21}\neq\frac{16}{21}$

Step4: Analyze third option

For a player on Team C to be 10 - year - old, number of 10 - year - old players on Team C is 5 and total number of players on Team C is 16. Probability = $\frac{5}{16}$

Step5: Analyze fourth option

For a 10 - year - old player to be on Team B, number of 10 - year - old players on Team B is 3 and total number of 10 - year - old players is 14. Probability = $\frac{3}{14}\neq\frac{13}{58}$

Answer:

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