For f(r) = sin(Tx) on [0, 1], find the Bernstein polynomials B1, B2, B3, B4. Simplify answers as much as is reasonable. |3D

Suppose that Pr[A|B]=12, Pr[A]=1324, and Pr[B′]=512. Find Pr[B|A′].

Suppose that Pr[A|B]=713, Pr[B|A]=711, and Pr[A′]=1021. Find Pr[A∩B′].

4. Let f(x) := r³ – 15x + 1. (a) Use the Intermediate Value Theorem to prove that f(x) has a root on the interval [-4,–3]. (b) Prove that ƒ has three real-valued roots. (Hint: You do not want to try and factor this or find the exact roots. Simply show that they exist.)