1. At a certain high school 25 students made high honors last term. Five of them were seniors and 6 were juniors. If one student will be selected at random from these 25 students to represent the school at a state conference, what is the probability that neither a senior nor a junior will be selected?
Answer: D
The probability that neither a senior nor a junior will be selected is 0.56.
To find the probability that neither a senior nor a junior will be selected, we first determine the number of students who are neither seniors nor juniors. With 5 seniors and 6 juniors among the 25 students, this leaves 14 students who are neither. Thus, the probability is calculated as 14 out of 25, which simplifies to 0.56.
A) 0.4
This option is incorrect because it suggests that 40% of the students selected would be neither seniors nor juniors. However, with 14 out of 25 students falling into this category, the correct probability is higher than 0.4.
B) 0.48
This option is also incorrect. A probability of 0.48 would imply that 48% of the students are neither seniors nor juniors, which does not align with the calculation that shows 56% of the students are in that category.
C) 0.52
This choice is incorrect as well. A probability of 0.52 indicates that only 52% of the students are neither seniors nor juniors, which underestimates the actual number of students in this category based on the provided details.
D) 0.56
This option is correct because it accurately represents the probability of selecting a student who is neither a senior nor a junior. With 14 students fitting this criteria out of a total of 25, the calculation confirms that the probability is indeed 0.56.
E) 0.6
This option is incorrect as it suggests that 60% of the students selected would be neither seniors nor juniors. This is not supported by the data, which shows a lower proportion of students in that category.
Conclusion
The correct answer is 0.56, reflecting the accurate probability of selecting a student who is neither a senior nor a junior from the group. All other options misrepresent this probability by either underestimating or overestimating the number of students who fit the criteria, thus confirming that D is the only correct choice.