A class has 12 boys and 18 girls. If two students are selected at random without replacement, what is the probability that both are girls?

Step 1: Find the total number of students.

12 + 18 = 30

There are 30 students total.

Step 2: Find the probability that the first student selected is a girl.

There are 18 girls among 30 students:

P(first girl) = 18/30

Step 3: Find the probability that the second student is a girl given that the first was a girl.

Because the selection is without replacement, there are now 17 girls remaining among 29 students.

P(second girl | first girl) = 17/29

Step 4: Multiply the probabilities.

P(both girls) = (18/30)(17/29)

Step 5: Simplify.

P(both girls) = 306/870
P(both girls) = 51/145

As a decimal:
51/145 ≈ 0.352

Therefore, the probability that both selected students are girls is 51/145, or approximately 0.352.