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Question Watch Video Show Examples In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class passed the test or completed the homework? Passed the test Failed the test Completed the homework 10 5 Did not complete the homework 3 4 Answer Attempt 3 out of 10 ◻ Submit Answer Log Out

Question\newlineWatch Video\newlineShow Examples\newlineIn a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class passed the test or completed the homework?\newline\begin{tabular}{|c|c|c|}\newline\hline & Passed the test & Failed the test \\\newline\hline Completed the homework & 1010 & 55 \\\newline\hline Did not complete the homework & 33 & 44 \\\newline\hline\newline\end{tabular}\newlineAnswer Attempt 33 out of 1010\newline□ \square \newlineSubmit Answer\newlineLog Out

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Q. Question\newlineWatch Video\newlineShow Examples\newlineIn a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class passed the test or completed the homework?\newline\begin{tabular}{|c|c|c|}\newline\hline & Passed the test & Failed the test \\\newline\hline Completed the homework & 1010 & 55 \\\newline\hline Did not complete the homework & 33 & 44 \\\newline\hline\newline\end{tabular}\newlineAnswer Attempt 33 out of 1010\newline□ \square \newlineSubmit Answer\newlineLog Out
  1. Calculate Total Students: First, we need to determine the total number of students in the class. We do this by adding up all the students in each category.\newlineTotal students =(Passed the test and Completed the homework)+(Failed the test and Completed the homework)+(Passed the test and Did not complete the homework)+(Failed the test and Did not complete the homework)= (\text{Passed the test and Completed the homework}) + (\text{Failed the test and Completed the homework}) + (\text{Passed the test and Did not complete the homework}) + (\text{Failed the test and Did not complete the homework})\newlineTotal students =10+5+3+4= 10 + 5 + 3 + 4\newlineTotal students =22= 22
  2. Calculate Passed Test or Completed Homework: Next, we calculate the number of students who passed the test or completed the homework. To avoid double-counting the students who both passed the test and completed the homework, we will add the number of students who passed the test to the number of students who completed the homework and then subtract the number of students who did both.\newlineNumber of students who passed the test or completed the homework =(Passed the test)+(Completed the homework)−(Passed the test and Completed the homework)= (\text{Passed the test}) + (\text{Completed the homework}) - (\text{Passed the test and Completed the homework})\newlineNumber of students who passed the test or completed the homework =(10+3)+(10+5)−10= (10 + 3) + (10 + 5) - 10\newlineNumber of students who passed the test or completed the homework =13+15−10= 13 + 15 - 10\newlineNumber of students who passed the test or completed the homework =28−10= 28 - 10\newlineNumber of students who passed the test or completed the homework =18= 18
  3. Calculate Probability: Now, we calculate the probability that a student chosen randomly from the class passed the test or completed the homework. The probability is the number of students who passed the test or completed the homework divided by the total number of students.\newlineProbability = Number of students who passed the test or completed the homework / Total students\newlineProbability = 1822\frac{18}{22}
  4. Simplify Probability: Finally, we simplify the fraction to get the probability in simplest form. \newlineProbability = 1822\frac{18}{22} \newlineProbability = 911\frac{9}{11}

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