According to the record of the registrar's office at a state university, 40% of the students are freshman, 25% are sophomore, 20% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 75%, 60%, 40%, and 30%.

If a randomly selected student does not live in the dormitory, what is the probability that the student is a junior?

4er

75

To find the probability that a randomly selected student, who does not live in the dormitory, is a junior, we need to consider the percentage of juniors out of the total population of students who do not live in the dormitory.

Let's break down the problem step by step:

1. Determine the percentage of students who do not live in the dormitory:
- The portion of dormitory residents among freshmen is 75%, so the percentage of freshmen who do not live in the dormitory is 100% - 75% = 25%.
- Similarly, the percentages of non-dormitory residents among sophomores, juniors, and seniors are 40%, 60%, and 70%, respectively.

2. Calculate the overall percentage of students who do not live in the dormitory:
- Since the percentages of students who do not live in the dormitory depend on their academic year, we need to consider each category's portion:
Freshmen: 25%
Sophomores: 40%
Juniors: 60%
Seniors: 70%
- We'll use these percentages to find the weighted average of students who do not live in the dormitory:
(0.25 * 40%) + (0.25 * 25%) + (0.20 * 60%) + (0.30 * 70%)
= 0.1 + 0.0625 + 0.12 + 0.21
= 0.4925 or 49.25%

3. Calculate the probability that a randomly selected student, who does not live in the dormitory, is a junior:
- The percentage of juniors who do not live in the dormitory is 60%.
- So, we'll divide the percentage of juniors who do not live in the dormitory by the overall percentage of students who do not live in the dormitory:
60% / 49.25%
= 0.60 / 0.4925
≈ 1.22 or 122%

Therefore, the probability that a randomly selected student, who does not live in the dormitory, is a junior is approximately 122%.