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Question
A card is drawn from a pack of 52 cards so the teach card is equally likely to be selected. In which of the following cases are the events A and B independent?
A = the card drawn is black, B = the card drawn is a king.
Solution
\[ P\left( \text{ black } \right) = P\left( A \right) = \frac{26}{52} = \frac{1}{2}\]
\[P\left( \text{ king } \right) = P\left( B \right) = \frac{4}{52} = \frac{1}{13}\]
\[P\left( A \cap B \right) = P\left( \text{ black king } \right) = \frac{2}{52} = \frac{1}{26}\]
\[P\left( A \cap B \right) = P\left( A \right) P\left( B \right)\]
\[\text{ Thus, A and B are independent events } .\]
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