For a course with two sections, let A denote \{first section is online\}, let \(B\) denote \{at least one section is online\}, and let \(\mathrm{C}\) denote \{both sections are online\}. Suppose \(\mathrm{P}\) \{a section is online \(\}=1 / 2\) and that the sections are independent.

a. Find \(\mathrm{P}(\mathrm{C} \mid \mathrm{A})\).

b. Are \(\mathrm{A}\) and \(\mathrm{C}\) independent events? Explain why or why not.

c. Find \(\mathrm{P}(\mathrm{C} \mid \mathrm{B})\).

d. Describe what makes \(\mathrm{P}(\mathrm{C} \mid \mathrm{A})\) and \(\mathrm{P}(\mathrm{C} \mid \mathrm{B})\) different from each other.