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In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays neither a sport nor an instrument?








Plays an


instrument







Does not play


an instrument









Plays a


sport




2
4

Question\newlineShow Examples\newlineIn a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays neither a sport nor an instrument?\newline\begin{tabular}{|c|c|c|}\newline\hline & \begin{tabular}{c} \newlinePlays an \\\newlineinstrument\newline\end{tabular} & \begin{tabular}{c} \newlineDoes not play \\\newlinean instrument\newline\end{tabular} \\\newline\hline \begin{tabular}{c} \newlinePlays a \\\newlinesport\newline\end{tabular} & 22 & 44 \\\newline\hline\newline\end{tabular}

Full solution

Q. Question\newlineShow Examples\newlineIn a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays neither a sport nor an instrument?\newline\begin{tabular}{|c|c|c|}\newline\hline & \begin{tabular}{c} \newlinePlays an \\\newlineinstrument\newline\end{tabular} & \begin{tabular}{c} \newlineDoes not play \\\newlinean instrument\newline\end{tabular} \\\newline\hline \begin{tabular}{c} \newlinePlays a \\\newlinesport\newline\end{tabular} & 22 & 44 \\\newline\hline\newline\end{tabular}
  1. Identify Categories: Identify the total number of students in each category from the data table.\newline- Students who play a sport and an instrument: 22\newline- Students who play a sport but do not play an instrument: 44\newline- Total students who play a sport (2+42 + 4): 66
  2. Calculate Total Students: Calculate the total number of students in the class.\newlineAssuming the table includes all students, and there are no students outside these categories, the total is just those who play a sport, as no data is given for those who don't play a sport.\newline- Total students in class: 66

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