Question

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.

What is the probability that a student did not get into their first-choice college based on the information provided?
A) 0.3875
B) 0.4125
C) 0.5175
D) 0.4625

Answer 1

The probability that a student did not get into their first-choice college is 0.605 or 60.5%. which is not included in the options given.

Step-by-step explanation:

To find the probability that a student did not get into their first-choice college based on the information provided, we need to calculate the probability of not being accepted for each AP science subject and then combine these probabilities. Let's calculate it step by step:

1. Calculate the percentage of seniors taking AP Chemistry who did not get accepted to their first-choice college: 100% - 45% = 55%.
2. Calculate the percentage of seniors taking AP Physics who did not get accepted to their first-choice college: 100% - 55% = 45%.
3. Calculate the percentage of seniors taking AP Environmental Science who did not get accepted to their first-choice college: 100% - 20% = 80%.
4. Since the remaining seniors take AP Biology, the percentage of seniors taking AP Biology who did not get accepted to their first-choice college is: 100% - 30% = 70%.
5. Now, we need to calculate the weighted average of these probabilities based on the percentage of students taking each subject:
   • (25% * 55%) + (35% * 45%) + (30% * 80%) + (10% * 70%) = 13.75% + 15.75% + 24% + 7%
   • = 60.5%

Therefore, the probability that a student did not get into their first-choice college based on the information provided is 0.605 or 60.5%.