  ### Home > INT2 > Chapter 8 > Lesson 8.3.1 > Problem8-60

8-60.

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 $(0.60)(0.10)$ $0.10$ Not senior $(0.20)$
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.

$25\%$

Use the alternative definition of independence (see the Math Notes box in Lesson 7.2.3) to determine if being a senior is associated with living in the OceanView dorm.

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