Students must take an AP Sciences exam their senior year:

- 25% take AP Chemistry
- 35% take AP Physics
- 30% take AP Environmental Science
- The remaining seniors take AP Biology

Of those who take AP Chemistry, 45% get accepted to their first-choice college, compared with:
- 55% who take AP Physics
- 20% who take AP Environmental Science
- 30% who take AP Biology

Use the tree diagram to determine the probability that a student did not get into their first-choice college. Enter your answer as a decimal to the ten-thousandths place.

The probability that a student did not get into their first-choice college, considering the percentages of students taking different AP Sciences exams and the corresponding acceptance rates, is 0.6050 or 60.50%.

Explanation:

The question involves calculating the probability of a student not getting into their first-choice college based on the probabilities associated with each AP Sciences exam they may take. To find this probability, we need to consider the percentage of students taking each AP exam and the percentage of those students who do not get accepted to their first-choice college.

Using a tree diagram, we can calculate the probability for each AP subject as follows:

AP Chemistry: 25% of seniors take it, and of these, 55% do not get accepted (100% - 45%).
AP Physics: 35% of seniors take it, and of these, 45% do not get accepted (100% - 55%).
AP Environmental Science: 30% of seniors take it, and of these, 80% do not get accepted (100% - 20%).
AP Biology: 10% of seniors take it (100% - 25% - 35% - 30%), and of these, 70% do not get accepted (100% - 30%).

The overall probability is the sum of the individual probabilities for each subject:

(25% * 55%) for AP Chemistry
(35% * 45%) for AP Physics
(30% * 80%) for AP Environmental Science
(10% * 70%) for AP Biology

We convert the percentages to decimals and sum them up:

P = (0.25 * 0.55) + (0.35 * 0.45) + (0.30 * 0.80) + (0.10 * 0.70) = 0.1375 + 0.1575 + 0.2400 + 0.0700 = 0.6050

Thus, the probability that a student did not get into their first-choice college is 0.6050, or 60.50% when converted back to a percentage.

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