n 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 5 3
Does not have an A 4 10

Answer 1

To find the probability that a randomly chosen student slept more than 6 hours and has an A, we can follow these steps:

1. Identify the relevant counts from the given table:

   • Students who slept more than 6 hours and have an A: 5
   • Students who slept 6 hours or less and have an A: 3
   • Students who do not have an A and slept more than 6 hours: 4
   • Students who do not have an A and slept 6 hours or less: 10

2. Calculate the total number of students:

   • Total with an A (more than 6 hours + 6 hours or less): \(5 + 3 = 8\)
   • Total without an A (more than 6 hours + 6 hours or less): \(4 + 10 = 14\)
   • Total number of students in the class: \(8 + 14 = 22\)

3. Calculate the probability:

   • We want the probability of a student who slept more than 6 hours and has an A, which is the number of students who slept more than 6 hours and have an A divided by the total number of students. \[ P(\text{sleeps more than 6 hours and has an A}) = \frac{\text{Number of students who slept more than 6 hours and have an A}}{\text{Total number of students}} = \frac{5}{22} \]

Thus, the probability that a randomly chosen student from the class slept more than 6 hours and has an A is \(\frac{5}{22}\).