Question: 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})

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.

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