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 } \\).

Explanation:

Step1: Calculate probability for each option

• Option 1: Probability that a randomly selected player on Team A is 8 years old.
• Formula: \(P=\frac{\text{Number of 8 - year - old on Team A}}{\text{Total number of players on Team A}}\)
• Substitute values: \(P=\frac{4}{15}

eq\frac{4}{21}\)

• Option 2: Probability that a randomly selected 8 - year - old player is on Team C.
• Formula: \(P = \frac{\text{Number of 8 - year - old on Team C}}{\text{Total number of 8 - year - old players}}\)
• Substitute values: \(P=\frac{8}{21}

eq\frac{16}{21}\)

• Option 3: Probability that a randomly selected player on Team C is 10 years old.
• Formula: \(P=\frac{\text{Number of 10 - year - old on Team C}}{\text{Total number of players on Team C}}\)
• Substitute values: \(P=\frac{5}{16}\)
• Option 4: Probability that a randomly selected 10 - year - old player is on Team B.
• Formula: \(P=\frac{\text{Number of 10 - year - old on Team B}}{\text{Total number of 10 - year - old players}}\)
• Substitute values: \(P=\frac{3}{14}

eq\frac{13}{58}\)

Answer:

The probability that a randomly selected player on Team C is 10 years old is \(\frac{5}{16}\) (Option 3).