Question: Conditional Probability: A box contains three white, two red, and one blue poker chips. Two chips are randomly chosen without replacement, and their colors noted. Define the following events:

A: {Both chips are the same color}

B: {Both chips are red}

C: {At least one chip is red or white}

1. Find \(\Pr \left( B|A \right)\). Is event B independent of event A?
2. Find \(\Pr \left( B|{{A}^{C}} \right)\). Is event B independent of event \({{A}^{C}}\) ?
3. Find \(\Pr \left( B|C \right)\). Is event B independent of event C?
4. Find \(\Pr \left( B|{{C}^{C}} \right)\). Is event A independent of event \({{C}^{C}}\) ?

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