Math  /  Data & Statistics

QuestionThe following table lists the ages and number of players per age group that are on a hockey team. Let A={A=\{ hockey players who are 12 years old }\}. How many players are in the complement of AA ? \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{\begin{tabular}{c} Ages of Players on \\ Hockey Team \end{tabular}} \\ \hline Age & Number of Players \\ \hline 9 & 2 \\ \hline 10 & 5 \\ \hline 11 & 9 \\ \hline 12 & 3 \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The set A A includes only hockey players who are 12 years old.
2. The complement of A A includes all players who are not 12 years old.

STEP 2

1. Calculate the total number of players.
2. Determine the number of players who are 12 years old.
3. Calculate the number of players in the complement of A A .

STEP 3

Calculate the total number of players by summing the number of players in each age group:
2+5+9+3=19 2 + 5 + 9 + 3 = 19

STEP 4

Determine the number of players who are 12 years old:
3 3

STEP 5

Calculate the number of players in the complement of A A by subtracting the number of 12-year-olds from the total number of players:
193=16 19 - 3 = 16
The number of players in the complement of A A is:
16 \boxed{16}

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