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# Conditional Probability

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# Conditional Probability - Answer Key

## Calculating College Acceptance using Conditional Probability

### Topic

Calculating College Acceptance using Conditional Probability

### Vocabulary

• Conditional probability

### Student Exploration

#### What are the chances you can get into the college of your dreams?

Getting into college is more difficult than it has ever been. More students are applying than ever before. This is causing many students to wonder what they need to do to get into the college of their dreams. So what are your chances of getting into the college of your dreams?

1. Research the admission requirements for a college of your choice. See below for a few examples. Unfortunately not all colleges supply this information; a hint for completing your research is to search for “student profiles” or “freshman profiles.” You can also call the college of your choice and ask an admission office representative.
2. Then look up the percentage of students that are admitted to college with different grade point averages (gpas), including your own gpa. Then calculate the probability you would be admitted to that college given that you have your gpa. For example: “If I have a 3.3 gpa, what are my chances of getting into UCLA if I apply?”
Let’s define $A$ as having a 3.3 gpa (weighted) and $B$ as chances of getting into UCLA if you apply. Then $P \left(\frac{A}{B}\right) = \frac{P(A \cap B)}{P(B)}=\frac{0.0277}{0.2548}=0.1087 \approx 10.9%$.
Because $P(B) = \frac{15689}{61566}=0.2548 \approx 25.48%$ as there were 15689 students that were admitted out of the 61566 students that applied and $P(A \cap B)= P(A \ and \ B) = \frac{286}{10314}=.0277 \approx 2.77%$, because 286 were admitted that had between a 3.3-3.69 gpa, out of 10314 students that applied with gpas in that range.
3. Next look up the percentage of students that are admitted to college with different SAT scores, you may also look up ACT scores. Look up the percentage of students that are admitted to college with your own SAT or ACT score. Then calculate the probability you would be admitted to that college given that you have your SAT score. For example: “If I got a 1630 composite score on the SAT, what are my chances of getting into UCLA if I apply?”
Let’s define $A$ as having a 1630 composite SAT score and $B$ as chances of getting into UCLA if you apply. Then $P \left(\frac{A}{B}\right) = \frac{P(A \cap B)}{(P(B)}=\frac{0.1194}{0.2548}=0.4686 \approx 46.9%$.
Because $P(B) = \frac{15689}{61566}=0.2548 \approx 25.48%$ as there were 15689 students that were admitted out of the 61566 students that applied and $P(A \cap B)= P(A \ and \ B) = \frac{1656}{13867}=0.1194 \approx 11.94%$, because 1,656 were admitted that had between a 1500-1790 composite SAT score, out of 13,867 students that applied with SAT scores in that range.
4. Lastly look up the percentage of students that are admitted to college with different high school course loads. Look up the percentage of students that are admitted to college with courses you have taken. Then calculate the probability you would be admitted to that college given your course load.
Let’s define $A$ as having a course load of 38 semesters of $A-G$ subject classes and $B$ as chances of getting into UCLA if you apply. Then $P\left(\frac{A}{B}\right) = \frac{P(A \cap B)}{P(B)}=\frac{0.0807}{0.2548}=0.3167 \approx 31.7%$.
Because $P(B) = \frac{15689}{61566}=0.2548 \approx 25.48%$ as there were 15689 students that were admitted out of the 61566 students that applied and $P(A \cap B)= P(A \ and \ B) = \frac{192}{2380}=0.0807 \approx 8.07%$ because 192 were admitted that had a course load of 38 semesters of $A-G$ subject classes, out of 2,380 students that applied with SAT scores in that range.

### Extension Investigation

What would happen if you had a better gpa, SAT score or course load?

1. Now go back and pretend that you have a higher gpa. Calculate the probability you would be admitted to that college given that you have that gpa.
2. Now go back and pretend that you have a higher SAT score. Calculate the probability you would be admitted to that college given that you have that SAT score.
3. Now go back and pretend that you take a more difficult course load. Calculate the probability you would be admitted to that college given that you have that course load.
4. Go back to the original question. What are your chances of getting into the college of your dream? What is one thing that you can do to improve your chances the most? What plays the biggest role in determining your college admission?

### Connections to other CK-12 Subject Areas

• Probability of Compound Events
• Theoretical and Experimental Probability
• Theoretical Probability
• Experimental Probability.