In a class of students, the following data table summarizes the amount of sleep of students and whether they have an A in the class. What is the probability that a student chosen randomly from the class is student who slept more than 6 hours who has an A?

Question

Slept more than 6 hours Slept 6 hours or less
Has an A 7 2
Does not have an A 6 13
Answer

Answer 1

To find the probability that a randomly chosen student from the class both slept more than 6 hours and has an A, we can use the data provided in the table.

From the table, we have the following information:

• Students who slept more than 6 hours and have an A: 7
• Students who slept 6 hours or less and have an A: 2
• Students who do not have an A and slept more than 6 hours: 6
• Students who do not have an A and slept 6 hours or less: 13

First, we need to calculate the total number of students in the class. This is done by summing all the categories from the table:

\[ \text{Total students} = (7 + 2) + (6 + 13) = 9 + 19 = 28 \]

Next, we find the number of students who slept more than 6 hours and have an A:

\[ \text{Students with A and slept more than 6 hours} = 7 \]

Now, we can calculate the probability \( P \) that a randomly chosen student is one who slept more than 6 hours and has an A:

\[ P(\text{More than 6 hours and has an A}) = \frac{\text{Number of students who slept more than 6 hours and has an A}}{\text{Total number of students}} = \frac{7}{28} \]

To simplify:

\[ P(\text{More than 6 hours and has an A}) = \frac{1}{4} \]

So, the probability that a randomly chosen student from the class is a student who slept more than 6 hours and has an A is \(\frac{1}{4}\) or 0.25.