To find the probability that a randomly chosen student from the class is a student who slept more than 6 hours and has an A, we can follow these steps:
1. Identify the specific group of interest and their count: We need the number of students who slept more than 6 hours and have an A. According to the given data table, there are [tex]\(7\)[/tex] such students.
2. Calculate the total number of students in the class: We sum up the number of students across all categories in the table:
- Students who slept more than 6 hours and have an A: [tex]\(7\)[/tex]
- Students who slept 6 hours or less and have an A: [tex]\(2\)[/tex]
- Students who slept more than 6 hours and do not have an A: [tex]\(6\)[/tex]
- Students who slept 6 hours or less and do not have an A: [tex]\(13\)[/tex]
Adding these values gives:
[tex]\[
7 + 2 + 6 + 13 = 28
\][/tex]
3. Determine the total number of students in the specific group (students who slept more than 6 hours and have an A): This is [tex]\(7\)[/tex], as found in step 1.
4. Compute the probability: The probability [tex]\(P\)[/tex] of a randomly chosen student being from the specific group is given by the ratio of the number of students in that group to the total number of students in the class:
[tex]\[
P(\text{student slept more than 6 hours and has an A}) = \frac{\text{Number of students who slept more than 6 hours and have an A}}{\text{Total number of students}} = \frac{7}{28}
\][/tex]
5. Simplify the fraction if possible: Simplifying [tex]\(\frac{7}{28}\)[/tex] gives:
[tex]\[
\frac{7}{28} = \frac{7 \div 7}{28 \div 7} = \frac{1}{4}
\][/tex]
Converting this to a decimal form, we get:
[tex]\[
\frac{1}{4} = 0.25
\][/tex]
Thus, the probability that a randomly chosen student from the class is a student who slept more than 6 hours and has an A is [tex]\(0.25\)[/tex] or [tex]\(25\%\)[/tex].
