A dice is rolled two times. Find the probability of getting a composite number on first roll and a prime number on second roll?

Number of composite numbers in a dice = 2 (4 and 6)
Hence, Probability of getting a composite number = $$\dfrac{2}{6} = \dfrac{1}{3}$$
Number of prime numbers in a dice = 3 (2, 3 and 5)
Hence, Probability of getting a prime number = $$\dfrac{3}{6} = \dfrac{1}{2}$$
Therefore, probability of getting a composite number on first roll and a prime number on second roll = $$\dfrac{1}{3}\times\dfrac{1}{2} = \dfrac{1}{6}$$