  ### Home > CCG > Chapter 10 > Lesson 10.3.5 > Problem10-176

10-176.

Of the students who choose to live on campus at Coastal College, $10$% are seniors. The most desirable dorm rooms are in the newly constructed OceanView dorm, and $60$% of the seniors live there, while $20$% of the rest of the students live there.

1. Represent these probabilities in a two-way table.

 Ocean View Not Ocean View Senior $(0.60)(0.10)=\mathbf{0.06}$ $0.10$ Not Senior $(0.20)\mathbf{(0.90)}=\mathbf{0.18}$ $1.00$
2. What is the probability that a randomly selected resident of the OceanView dorm is a senior?

Compare the percentage of seniors who live in OceanView to the percentage of total students who live in OceanView.

$25\%$

3. Use the alternative definition of independence (see the Math Notes box in Lesson 10.2.3) to determine if being a senior is associated with living in the Ocean View dorm.

If events $\text{A}$ and $\text{B}$ are independent, then $\text{P}(\text{A and B})=\text{P}(\text{A})·P(\text{B})$.
The converse of this statement is also true: $\text{P}(\text{A and B})=\text{P}(\text{A})·P(\text{B})$, then $\text{A}$ and $\text{B}$ are independent.