What is the probability of getting a composite number on the first roll of a die and getting a prime number on the second roll?

Well, the prime #s between 1 and 6 are 1,2,3, and 5. The composite #s are 4, and 6.

The chance of a comp. on the 1st roll is 2/6, or 1/3. The chance of getting a prime number is 4/6, or 2/3. Multiply these two together to get your answer. The denominators are 3s, so they multiply to give you 9, and 2*1 equals 2, giving you 2/9.