To address the given question:
1. Identify the Relevant Information:
- The professor found that 50% of her students pass the final exam.
- She gives the exam during the fall, spring, and summer terms.
- Each term has 30 students.
- We are interested in knowing the chances of a student passing the exam during the fall term.
2. Understand the Concept of Simulation:
- Using a fair coin flip to simulate the chance of a student passing or failing the exam, where "heads" could represent passing (50% chance), and "tails" could represent failing (50% chance).
- Rolling a number cube with equal chances for each outcome doesn't represent the 50% success rate directly without additional conditions or constraints.
3. Determine the Appropriate Simulation Method:
- Flipping a coin 30 times will allow us to simulate each student's outcome for the fall term, with each flip representing one student.
Let's evaluate each provided method:
1. Flip 30 times and count the number of times you land on heads:
- This method simulates each of the 30 students, with a 50% chance of passing the exam.
- This counts the number of students who passed in the fall term correctly (each flip is independent and has a 50% success probability).
2. Roll 30 times and count the number of times you roll a 4:
- Rolling a cube does not provide an equal simulation for the 50% chance (since each side of the cube has a 1/6 chance).
3. Flip 90 times and count the number of times you land on heads:
- This seems to simulate multiple terms (30 students each x 3 terms), but may confuse the specific term we’re interested in (fall term).
- There's no need to consider students outside of the fall term if the question is specific to the fall term.
4. Roll 90 times and count the number of times you roll a 4:
- Same issue as before, rolling a 4 has a 1/6 chance and does not simulate a 50% success rate.
5. Flip and roll 90 times, and record when you land on heads and roll greater than 2:
- This combined method creates unnecessary complexity and doesn't target the specific interest point (fall term and the 50% pass rate).
Best Method:
Since the question specifies the chance of a student passing the exam during the fall term, flipping the coin 30 times and counting the number of times you land on heads is the most straightforward and accurate way to simulate the 50% passing rate for the 30 students in the fall term.
Thus, the correct simulation method to use is:
\begin{tabular}{|c|c|}
\hline Method & Count the number of times you... \\
\hline
Flip 30 times. & Land on heads. \\
\hline
\end{tabular}
