The problem asks for the probability that at least one of the 18 students selects a U.S. president who died in office.

To solve this, we will use the complement rule, which is often easier in "at least one" problems.

Step-by-Step Solution:

1. Complement Probability: First, we calculate the probability that none of the students select a president who died in office. We subtract this from 1 to get the probability that at least one does.

2. Basic Setup:

   • There are 43 U.S. presidents, and 8 of them died in office.
   • The probability of selecting a president who did not die in office is: $P(\text{no death}) = \frac{43 - 8}{43} = \frac{35}{43}$

3. No Student Picks a Deceased President: If no student picks a president who died in office, all 18 students must pick from the 35 who didn't. The probability that all 18 students avoid picking a deceased president is: $P(\text{no death for all 18}) = \left( \frac{35}{43} \right)^{18}$

4. Complement (At Least One Death): Now, the probability that at least one student picks a president who died in office is: $P(\text{at least one death}) = 1 - \left( \frac{35}{43} \right)^{18}$

5. Calculation: Let's compute: $\frac{35}{43} \approx 0.81395$ Then, raise this to the 18th power: $0.81395^{18} \approx 0.0401$ Finally, subtract from 1: $P(\text{at least one death}) = 1 - 0.0401 = 0.9599$

Final Answer:

The probability that at least one student selects a president who died in office is approximately 0.96 (rounded to the nearest hundredth).

Would you like more details or have any questions? Here are some follow-up questions:

1. How is the complement rule useful in probability problems?
2. What happens to the probability if the number of students increases?
3. How does the probability change if fewer presidents had died in office?
4. Can you explain why we used powers of probability in this solution?
5. What if there were restrictions on the number of times a president could be chosen?

Tip: The complement rule simplifies many "at least one" problems by shifting focus to the opposite scenario.