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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 a king or queen, B = the card drawn is a queen or jack.
Solution
\[P\left( \text{ king or queen } \right) = P\left( A \right) = \frac{8}{52} = \frac{2}{13}\]
\[P\left( \text{ queen or jack } \right) = P\left( B \right) = \frac{8}{52} = \frac{2}{13}\]
\[P\left( A \cap B \right) = P\left( \text{ queen } \right) = \frac{4}{52} = \frac{1}{13}\]
\[P\left( A \cap B \right) \neq P\left( A \right) P\left( B \right)\]
\[\text{ Thus, A and B are not independent events.} \]
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