### Home > CCG > Chapter 6 > Lesson 6.1.3 > Problem6-28

6-28.

There are $212$ students enrolled in geometry at West Valley High School. $64$ are freshman, and $112$ are sophomores.

1. If a random geometry student is chosen, what is the chance (in percent) the student is a freshman or sophomore? Show how you can use the Addition Rule to answer this question. What was unusual about using the Addition Rule to answer this question?

Addition Rule: $P(\text{A or B}) = P(\text{A}) + P(\text{B}) − P(\text{A and B})$

$\frac{176}{212}\approx83\%$
The unusual part is that the probability of $A$ and $B$ (the overlap) was $0$.

2. $114$ of the geometry students perform in band and $56$ perform in chorus. There is a $75\%$ chance that a geometry student performs in either band or chorus. What is the probability a geometry student performs both in band and in chorus?

Use the Addition Rule again but this time you will need to solve the equation.