Answer to Question #314462 in Statistics and Probability for Mari bless

Question

Suppose F is a σ − algebra of subsets of Ω and let B ∈ F.

(a) Show that {A ∩ B : A ∈ F} is a σ − algebra of subsets of B

(b) If the sum of possible outcomes of a fair die thrown twice is ω and the sample

space Ω = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and B = {2, 4, 6, 8, 10} ∈ F, then deduce

that for any subset A of Ω, {A ∩ B : A ∈ F} is σ − algbra of subset of B