a) What is the percent likelihood that a random polynomial over $\displaystyle F_2 $ of degree exactly 10 factors into a product of polynomials of degree less than or equal to 2? What is the likelihood that a random nonzero polynomial of degree at most 10 factors into such a product?

(b) What is the probability that a random monic polynomial over $\displaystyle F_3 $ of degree exactly 10 factors into a product of polynomials of degree less than or equal to 2? What is the probability that a random monic polynomial of degree at most 10 factors into such a product?