Question

using tree diagrams to solve complex probabilities
students must take an ap sciences exam their senior year: 25% take ap chemistry, 35% take ap physics, 30% take ap environmental science and 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, and 30% who take ap biology.
use the partially completed tree diagram to fill in the indicated labels.

Explanation:

Step1: Calculate the percentage of students taking AP Biology

The sum of the percentages of students taking AP Chemistry, AP Physics, and AP Environmental Science is \(25\%+35\% + 30\%=90\%\).
The percentage of students taking AP Biology is \(100\% - 90\%=10\%\).

Step2: Analyze the labels

Label 1: The first - level branches represent the AP Science exams. The second - level branches represent the acceptance to the first - choice college.
Label 2: For the "Environmental Science" branch (Label 3), the probability of taking AP Environmental Science is \(0.30\) (Label 4). The probability of getting accepted to the first - choice college for AP Environmental Science is \(20\% = 0.20\).

Answer:

Label 1: AP Biology; Label 2: 1st choice; Label 3: environmental science; Label 4: \(0.30\); Label 5: \(0.20\)