Question

for a certain class, the following data table summarizes the amount of sleep of students and whether or not they have an a in the class. what is the probability that a student chosen randomly from the class slept more than 6 hours?

	slept more than 6 hours	slept 6 hours or less
does not have an a	6	10

Explanation:

Step1: Find total number of students

To find the total number of students, we sum up all the values in the table. The values are 8 (has an A, slept more than 6 hours), 4 (has an A, slept 6 hours or less), 6 (does not have an A, slept more than 6 hours), and 10 (does not have an A, slept 6 hours or less). So total students = \(8 + 4 + 6 + 10\) = \(28\).

Step2: Find number of students who slept more than 6 hours

The number of students who slept more than 6 hours is the sum of those who have an A and slept more than 6 hours and those who do not have an A and slept more than 6 hours. So that's \(8 + 6\) = \(14\).

Step3: Calculate the probability

Probability is the number of favorable outcomes (slept more than 6 hours) divided by the total number of outcomes (total students). So probability = \(\frac{14}{28}\) = \(\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)