syaoranig
Answered

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In a class of students, the following data table summarizes the amount of sleep of students and whether they have an [tex]$A$[/tex] in the class. What is the probability that a student chosen randomly from the class has an A?

\begin{tabular}{|c|c|c|}
\hline & \begin{tabular}{c}
Slept more \\
than 6 hours
\end{tabular} & \begin{tabular}{c}
Slept 6 \\
hours or \\
less
\end{tabular} \\
\hline Has an A & 4 & 3 \\
\hline \begin{tabular}{c}
Does not \\
have an A
\end{tabular} & 8 & 12 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
Let's analyze the given data step-by-step to find the probability that a randomly chosen student from the class has an A.

1. Identify the given data:
- Students who have an A and slept more than 6 hours: 4
- Students who have an A and slept 6 hours or less: 3
- Students who do not have an A and slept more than 6 hours: 8
- Students who do not have an A and slept 6 hours or less: 12

2. Calculate the total number of students who have an A:
- Students who have an A and slept more than 6 hours: 4
- Students who have an A and slept 6 hours or less: 3
- Total students who have an A = 4 + 3 = 7

3. Calculate the total number of students in the class:
- Students who have an A (total): 7
- Students who do not have an A and slept more than 6 hours: 8
- Students who do not have an A and slept 6 hours or less: 12
- Total students in the class = 7 + 8 + 12 = 27

4. Calculate the probability that a randomly chosen student has an A:
- Probability = (Total number of students who have an A) / (Total number of students in the class)
- Probability = 7 / 27

Thus, the probability that a randomly chosen student from the class has an A is approximately [tex]\( \frac{7}{27} \)[/tex] or [tex]\( 0.259 \)[/tex] (rounded to three decimal places).
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