Question

dana surveyed students in her class. she found that 8 earned an a, 6 earned a b, 4 earned a c, and 2 earned a d on the last science test. if she randomly surveys one more student from the class, what is the experimental probability that the student would have earned an a on the test?

Explanation:

Step1: Find total number of students

First, we need to find the total number of students surveyed. We add the number of students who earned each grade: \(8 + 6 + 4 + 2\). Let's calculate that: \(8+6 = 14\), \(14 + 4 = 18\), \(18 + 2 = 20\). So the total number of students is 20.

Step2: Calculate the probability of earning an A

The probability of an event is the number of favorable outcomes (students who earned an A) divided by the total number of outcomes (total number of students). The number of students who earned an A is 8, and the total number of students is 20. So the probability \(P(A)=\frac{8}{20}\). We can simplify this fraction by dividing both the numerator and the denominator by 4: \(\frac{8\div4}{20\div4}=\frac{2}{5}\). Wait, no, wait. Wait, 8 divided by 20: let's check again. Wait, 8/20 simplifies to 2/5? Wait, 8 divided by 4 is 2, 20 divided by 4 is 5. Yes. Wait, but let's check the original numbers again. The problem says: 8 earned an A, 6 earned a B, 4 earned a C, and 2 earned a D. So total is 8+6+4+2=20. So the number of students who earned an A is 8. So the probability is 8/20, which simplifies to 2/5? Wait, no, 8 divided by 20: 8 ÷ 20 = 0.4, and 2/5 is 0.4. Wait, but let's check the options. Wait, maybe I made a mistake. Wait, the options are 1/4, 2/5, 3/10, 2/3? Wait, no, the user's image shows options, but let's re-express. Wait, 8 students with A, total 20. So 8/20 = 2/5. So the probability is 2/5.

Answer:

\(\frac{2}{5}\) (assuming the option with 2/5 is the correct one)